/* file nfa.c  8.9.97.
 *
 * 25/9/98 added parameter subsets to nfa_determinize.
 * 2/10/97 - added version of nfa_determinize for compactly stored
 * transition tables.
 * This file contains routines for processing nfa's i.e. non-deterministic
 * finite state automata.
 * Currently, the only routine available is nfa_determinize, which returns
 * an equivalent deterministic automaton, whose states are subsets of the
 * input fsa.
 * Currently, the only input format accepted is sparse, where epsilon
 * transitions are from generator 0.
 */

#include <stdio.h>
#include "defs.h"
#include "fsa.h"
#include "hash.h"
#include "externals.h"
/* the following three definitions are for use in extracting edge-label
 * and state in compactly stored pairs.
 */
#define SHIFT 24
#define MASKR (unsigned) 0xffffff
#define MASKL (unsigned) 0xff000000

/* Functions defined in this file: */
fsa *nfa_determinize();
fsa *nfa_determinize_short();
fsa *nfa_determinize_int();
fsa *nfa_cdeterminize();
fsa *nfa_cdeterminize_short();
fsa *nfa_cdeterminize_int();
fsa *nfa_exists();
fsa *nfa_exists_short();
fsa *nfa_exists_int();

/* Functions used in this file and defined elsewhere */
void fsa_init();
void fsa_table_init();
void fsa_set_is_accepting();
void srec_copy();
void fsa_clear();
void hash_init();
void short_hash_init();
int  hash_locate();
int  short_hash_locate();
void hash_clear();
void short_hash_clear();
int* hash_rec();
unsigned short* short_hash_rec();
int hash_rec_len();
int short_hash_rec_len();

fsa *
nfa_determinize(fsaptr,op_table_type,eps_trans,destroy,subsets,tempfilename)
	fsa *fsaptr;
	storage_type op_table_type;
	boolean eps_trans;
	boolean destroy;
        boolean subsets;
	char *tempfilename;
/* The fsa *fsaptr must be an fsa with sparse table.
 * The returned fsa accepts the same language but is deterministic.
 * If eps_trans is false, it is assumed that *fsaptr has no epsilon
 * transitions.
 * If subsets is true, then the returned fsa will have state-set of type
 * "list of integers", where the list represents the subset of the state-set
 * of *fsaptr that correponds to the state of the returned fsa.
 */
{
  if (kbm_print_level>=3)
    printf("    #Calling nfa_determinize.\n");
  if (fsaptr->states->size < MAXUSHORT)
    return nfa_determinize_short(
              fsaptr,op_table_type,eps_trans,destroy,subsets,tempfilename);
  else
    return nfa_determinize_int(
               fsaptr,op_table_type,eps_trans,destroy,subsets,tempfilename);
}

fsa *
nfa_determinize_short(fsaptr,op_table_type,eps_trans,destroy,subsets,
			tempfilename)
	fsa *fsaptr;
	storage_type op_table_type;
	boolean eps_trans;
	boolean destroy;
        boolean subsets;
	char *tempfilename;
{
  int **table, *tableptr, *tableptre, ngens, nssi, nsi, ns, *fsarow,
      nt, cstate, csi, im, i, g1, len, ct, n;
  unsigned short *ht_ptr, *ht_chptr, *ht_ptrb, *ht_ptre,
                 *cs_ptr, *cs_ptre, *ptr;
  boolean dense_op;
  short_hash_table ht;
  fsa *det;
  FILE *tempfile, *fopen();

  if (kbm_print_level>=3)
    printf("    #Calling nfa_determinize_short.\n");

  tmalloc(det,fsa,1);
  fsa_init(det);
  srec_copy(det->alphabet,fsaptr->alphabet);
  det->flags[DFA] = TRUE;
  det->flags[ACCESSIBLE] = TRUE;
  det->flags[BFS] = TRUE;

  det->states->type = subsets ? LISTOFINTS : SIMPLE;

  det->table->table_type = op_table_type;
  det->table->denserows = 0;
  det->table->printing_format = op_table_type;

  if (fsaptr->num_initial==0) {
    det->num_initial = 0;
    det->num_accepting = 0;
    det->states->size = 0;
    if (destroy)
      fsa_clear(fsaptr);
    return det;
  }
  ngens = det->alphabet->size;
  nsi = fsaptr->states->size;

  fsa_set_is_accepting(fsaptr);

  dense_op = op_table_type==DENSE;
  table = fsaptr->table->table_data_ptr;

  det->num_initial = 1;
  tmalloc(det->initial,int,2);
  det->initial[1] = 1;
  
  short_hash_init(&ht,FALSE,0,0,0);
  ht_ptrb = ht.current_ptr;
  ht_ptre = ht_ptrb-1;
  nssi = fsaptr->num_initial;
  for (i=0;i<nssi;i++)
    *(++ht_ptre) = fsaptr->initial[i+1];
  /* now perform epsilon closure of initial subset */
  ptr=ht_ptrb-1;
  if (eps_trans)
  while (++ptr<=ht_ptre) {
    tableptr=table[*ptr]; tableptre=table[*ptr+1];
    while (tableptr < tableptre){
      if (*tableptr==0) {
        csi = *(tableptr+1);
        if (csi==0){
          tableptr+=2;
          continue;
        }
        if (csi> *ht_ptre) {
    /* We have a new state for the image subset to be added to the end */
          *(++ht_ptre) = csi;
        }
        else {
          ht_chptr = ht_ptrb;
          while (*ht_chptr < csi)
            ht_chptr++;
          if (csi < *ht_chptr) {
    /* we have a new state for the image subset to be added in the middle */
            ht_ptr = ++ht_ptre;
            while (ht_ptr > ht_chptr) {
              *ht_ptr = *(ht_ptr-1);
              ht_ptr--;
            }
            *ht_ptr = csi;
	    if (ptr > ht_ptr)
              ptr = ht_ptr-1;
          }
        }
      }
      tableptr+=2;
    }
  }
  im = short_hash_locate(&ht,ht_ptre-ht_ptrb+1);
/* Each state in 'det' will be represented as a subset of the set of states
 * of *fsaptr. The initial state contains the initial states
 * of *fsaptr.
 * A subset is an accept-state if it contains an accept state of *fsaptr
 * The subsets will be stored as variable-length records in the hash-table,
 * always in increasing order.
 */
  if (im!=1) {
    fprintf(stderr,"Hash-initialisation problem in nfa_determinize.\n");
    return 0;
  }
  if ((tempfile=fopen(tempfilename,"w"))==0){
    fprintf(stderr,"Error: cannot open file %s\n",tempfilename);
    return 0;
  }
  if (dense_op)
    tmalloc(fsarow,int,ngens)
  else
    tmalloc(fsarow,int,2*ngens+1)
 
  cstate = 0;
  if (dense_op)
    len = ngens; /* The length of the fsarow output. */
  nt = 0; /* Number of transitions in det */

  while (++cstate <= ht.num_recs) {
    if (kbm_print_level>=3) {
      if ((cstate<=1000 && cstate%100==0)||(cstate<=10000 && cstate%1000==0)||
          (cstate<=100000 && cstate%5000==0) || cstate%50000==0)
       printf("    #cstate = %d;  number of states = %d.\n",cstate,ht.num_recs);
    }
    cs_ptr = short_hash_rec(&ht,cstate);
    cs_ptre = short_hash_rec(&ht,cstate) + short_hash_rec_len(&ht,cstate) - 1;
    if (!dense_op)
      len = 0;

    for (g1=1;g1<=ngens;g1++) {
/* Calculate action of generator g1 on state cstate  - to get the image, we
 * simply apply it to each state in the subset of states representing cstate.
 */
      ht_ptrb = ht.current_ptr;
      ht_ptre = ht_ptrb-1;
      ptr = cs_ptr-1;
      while (++ptr <= cs_ptre) {
        tableptr=table[*ptr]; tableptre=table[*ptr+1]; 
        while (tableptr < tableptre){
          if (*tableptr==g1) {
            csi = *(tableptr+1);
            if (csi==0){
              tableptr+=2;
              continue;
            }
            if (ht_ptrb>ht_ptre || csi> *ht_ptre) {
    /* We have a new state for the image subset to be added to the end */
              *(++ht_ptre) = csi;
            }
            else {
              ht_chptr = ht_ptrb;
              while (*ht_chptr < csi)
                ht_chptr++;
              if (csi < *ht_chptr) {
    /* we have a new state for the image subset to be added in the middle */
                ht_ptr = ++ht_ptre;
                while (ht_ptr > ht_chptr) {
                  *ht_ptr = *(ht_ptr-1);
                  ht_ptr--;
                }
                *ht_ptr = csi;
              }
            }
          }
          tableptr+=2;
        }
      }
      /* now perform epsilon closure of image subset */
      ptr=ht_ptrb-1;
      if (eps_trans)
      while (++ptr<=ht_ptre) {
        tableptr=table[*ptr]; tableptre=table[*ptr+1];
        while (tableptr < tableptre){
          if (*tableptr==0) {
            csi = *(tableptr+1);
            if (csi==0){
              tableptr+=2;
              continue;
            }
            if (csi> *ht_ptre) {
    /* We have a new state for the image subset to be added to the end */
              *(++ht_ptre) = csi;
            }
            else {
              ht_chptr = ht_ptrb;
              while (*ht_chptr < csi)
                ht_chptr++;
              if (csi < *ht_chptr) {
    /* we have a new state for the image subset to be added in the middle */
                ht_ptr = ++ht_ptre;
                while (ht_ptr > ht_chptr) {
                  *ht_ptr = *(ht_ptr-1);
                  ht_ptr--;
                }
                *ht_ptr = csi;
	        if (ptr > ht_ptr)
                  ptr = ht_ptr-1;
              }
            }
          }
          tableptr+=2;
        }
      }
      im = short_hash_locate(&ht,ht_ptre-ht_ptrb+1);
      if (dense_op)
         fsarow[g1-1] = im;
      else if (im>0) {
         fsarow[++len] = g1;
         fsarow[++len] = im;
      }
      if (im>0)
        nt++;
    }
    if (!dense_op)
      fsarow[0] = len++;
    fwrite((void *)fsarow,sizeof(int),(size_t)len,tempfile);
  }
  fclose(tempfile);

  ns = det->states->size = ht.num_recs;
  det->table->numTransitions = nt;

/* Locate the accept states. A state is an accept state if and only if
 * the subset representing it contains an accept state of *fsaptr.
 * Also, if subsets is true, record the states in the intlist field
 * of det->states.
 */
  tmalloc(det->is_accepting,boolean,ns+1);
  for (i=1;i<=ns;i++)
    det->is_accepting[i] = FALSE;
  if (subsets)
    tmalloc(det->states->intlist,int *,ns+1);
  ct = 0;
  for (cstate=1;cstate<=ns;cstate++) {
    len = short_hash_rec_len(&ht,cstate);
    cs_ptr = short_hash_rec(&ht,cstate);
    cs_ptre = short_hash_rec(&ht,cstate) + len - 1;
/* See if the set contains an accept-state */
    ptr = cs_ptr-1;
    while (++ptr <= cs_ptre) if (fsaptr->is_accepting[*ptr]) {
      det->is_accepting[cstate] = TRUE;
      ct++;
      break;
    }
    if (subsets) {
      tmalloc(det->states->intlist[cstate],int,len+1);
      det->states->intlist[cstate][0]=len;
      n=0;
      ptr = cs_ptr-1;
      while (++ptr <= cs_ptre)
        det->states->intlist[cstate][++n] = *ptr;
    }
  }

  det->num_accepting = ct;
  if (ct==1 || ct != ns) {
    tmalloc(det->accepting,int,ct+1);
    ct = 0;
    for (i=1;i<=ns;i++) if (det->is_accepting[i])
      det->accepting[++ct] = i;
  }
  tfree(fsaptr->is_accepting);
  tfree(det->is_accepting);
  short_hash_clear(&ht);
  tfree(fsarow);

  if (destroy)
    fsa_clear(fsaptr);

/* Now read the transition table back in */
  tempfile = fopen(tempfilename,"r");
  compressed_transitions_read(det,tempfile);
  fclose(tempfile);

  unlink(tempfilename);

  return det;
}

fsa *
nfa_determinize_int(fsaptr,op_table_type,eps_trans,destroy,subsets,
			tempfilename)
	fsa *fsaptr;
	storage_type op_table_type;
	boolean eps_trans;
	boolean destroy;
        boolean subsets;
	char *tempfilename;
{
  int **table, *tableptr, *tableptre, ngens, nssi, nsi, ns, *fsarow,
      nt, cstate, csi, im, i, g1, len, ct, n;
  int *ht_ptr, *ht_chptr, *ht_ptrb, *ht_ptre,
                 *cs_ptr, *cs_ptre, *ptr;
  boolean dense_op;
  hash_table ht;
  fsa *det;
  FILE *tempfile, *fopen();

  if (kbm_print_level>=3)
    printf("    #Calling nfa_determinize_int.\n");

  tmalloc(det,fsa,1);
  fsa_init(det);
  srec_copy(det->alphabet,fsaptr->alphabet);
  det->flags[DFA] = TRUE;
  det->flags[ACCESSIBLE] = TRUE;
  det->flags[BFS] = TRUE;

  det->states->type = subsets ? LISTOFINTS : SIMPLE;

  det->table->table_type = op_table_type;
  det->table->denserows = 0;
  det->table->printing_format = op_table_type;

  if (fsaptr->num_initial==0) {
    det->num_initial = 0;
    det->num_accepting = 0;
    det->states->size = 0;
    if (destroy)
      fsa_clear(fsaptr);
    return det;
  }
  ngens = det->alphabet->size;
  nsi = fsaptr->states->size;

  fsa_set_is_accepting(fsaptr);

  dense_op = op_table_type==DENSE;
  table = fsaptr->table->table_data_ptr;

  det->num_initial = 1;
  tmalloc(det->initial,int,2);
  det->initial[1] = 1;
  
  hash_init(&ht,FALSE,0,0,0);
  ht_ptrb = ht.current_ptr;
  ht_ptre = ht_ptrb-1;
  nssi = fsaptr->num_initial;
  for (i=0;i<nssi;i++)
    *(++ht_ptre) = fsaptr->initial[i+1];
  /* now perform epsilon closure of initial subset */
  ptr=ht_ptrb-1;
  if (eps_trans)
  while (++ptr<=ht_ptre) {
    tableptr=table[*ptr]; tableptre=table[*ptr+1];
    while (tableptr < tableptre) {
      if (*tableptr==0) {
        csi = *(tableptr+1);
        if (csi==0) {
          tableptr+=2;
          continue;
        }
        if (csi> *ht_ptre) {
    /* We have a new state for the image subset to be added to the end */
          *(++ht_ptre) = csi;
        }
        else {
          ht_chptr = ht_ptrb;
          while (*ht_chptr < csi)
            ht_chptr++;
          if (csi < *ht_chptr) {
    /* we have a new state for the image subset to be added in the middle */
            ht_ptr = ++ht_ptre;
            while (ht_ptr > ht_chptr) {
              *ht_ptr = *(ht_ptr-1);
              ht_ptr--;
            }
            *ht_ptr = csi;
	    if (ptr > ht_ptr)
              ptr = ht_ptr-1;
          }
        }
      }
      tableptr+=2;
    }
  }
  im = hash_locate(&ht,ht_ptre-ht_ptrb+1);
/* Each state in 'det' will be represented as a subset of the set of states
 * of *fsaptr. The initial state contains the initial states
 * of *fsaptr.
 * A subset is an accept-state if it contains an accept state of *fsaptr
 * The subsets will be stored as variable-length records in the hash-table,
 * always in increasing order.
 */
  if (im!=1) {
    fprintf(stderr,"Hash-initialisation problem in nfa_determinize.\n");
    return 0;
  }
  if ((tempfile=fopen(tempfilename,"w"))==0){
    fprintf(stderr,"Error: cannot open file %s\n",tempfilename);
    return 0;
  }
  if (dense_op)
    tmalloc(fsarow,int,ngens)
  else
    tmalloc(fsarow,int,2*ngens+1)
 
  cstate = 0;
  if (dense_op)
    len = ngens; /* The length of the fsarow output. */
  nt = 0; /* Number of transitions in det */

  while (++cstate <= ht.num_recs) {
    if (kbm_print_level>=3) {
      if ((cstate<=1000 && cstate%100==0)||(cstate<=10000 && cstate%1000==0)||
          (cstate<=100000 && cstate%5000==0) || cstate%50000==0)
       printf("    #cstate = %d;  number of states = %d.\n",cstate,ht.num_recs);
    }
    cs_ptr = hash_rec(&ht,cstate);
    cs_ptre = hash_rec(&ht,cstate) + hash_rec_len(&ht,cstate) - 1;
    if (!dense_op)
      len = 0;

    for (g1=1;g1<=ngens;g1++) {
/* Calculate action of generator g1 on state cstate  - to get the image, we
 * simply apply it to each state in the subset of states representing cstate.
 */
      ht_ptrb = ht.current_ptr;
      ht_ptre = ht_ptrb-1;
      ptr = cs_ptr-1;
      while (++ptr <= cs_ptre) {
        tableptr=table[*ptr]; tableptre=table[*ptr+1]; 
        while (tableptr < tableptre) {
          if (*tableptr==g1) {
            csi = *(tableptr+1);
            if (csi==0) {
              tableptr+=2;
              continue;
            }
            if (ht_ptrb>ht_ptre || csi> *ht_ptre) {
    /* We have a new state for the image subset to be added to the end */
              *(++ht_ptre) = csi;
            }
            else {
              ht_chptr = ht_ptrb;
              while (*ht_chptr < csi)
                ht_chptr++;
              if (csi < *ht_chptr) {
    /* we have a new state for the image subset to be added in the middle */
                ht_ptr = ++ht_ptre;
                while (ht_ptr > ht_chptr) {
                  *ht_ptr = *(ht_ptr-1);
                  ht_ptr--;
                }
                *ht_ptr = csi;
              }
            }
          }
          tableptr+=2;
        }
      }
      /* now perform epsilon closure of image subset */
      ptr=ht_ptrb-1;
      if (eps_trans)
      while (++ptr<=ht_ptre) {
        tableptr=table[*ptr]; tableptre=table[*ptr+1];
        while (tableptr < tableptre) {
          if (*tableptr==0) {
            csi = *(tableptr+1);
            if (csi==0) {
              tableptr+=2;
              continue;
            }
            if (csi> *ht_ptre) {
    /* We have a new state for the image subset to be added to the end */
              *(++ht_ptre) = csi;
            }
            else {
              ht_chptr = ht_ptrb;
              while (*ht_chptr < csi)
                ht_chptr++;
              if (csi < *ht_chptr) {
    /* we have a new state for the image subset to be added in the middle */
                ht_ptr = ++ht_ptre;
                while (ht_ptr > ht_chptr) {
                  *ht_ptr = *(ht_ptr-1);
                  ht_ptr--;
                }
                *ht_ptr = csi;
	        if (ptr > ht_ptr)
                  ptr = ht_ptr-1;
              }
            }
          }
          tableptr+=2;
        }
      }
      im = hash_locate(&ht,ht_ptre-ht_ptrb+1);
      if (dense_op)
         fsarow[g1-1] = im;
      else if (im>0) {
         fsarow[++len] = g1;
         fsarow[++len] = im;
      }
      if (im>0)
        nt++;
    }
    if (!dense_op)
      fsarow[0] = len++;
    fwrite((void *)fsarow,sizeof(int),(size_t)len,tempfile);
  }
  fclose(tempfile);

  ns = det->states->size = ht.num_recs;
  det->table->numTransitions = nt;

/* Locate the accept states. A state is an accept state if and only if
 * the subset representing it contains an accept state of *fsaptr.
 * Also, if subsets is true, record the states in the intlist field
 * of det->states.
 */
  tmalloc(det->is_accepting,boolean,ns+1);
  for (i=1;i<=ns;i++)
    det->is_accepting[i] = FALSE;
  if (subsets)
    tmalloc(det->states->intlist,int *,ns+1);
  ct = 0;
  for (cstate=1;cstate<=ns;cstate++) {
    len = hash_rec_len(&ht,cstate);
    cs_ptr = hash_rec(&ht,cstate);
    cs_ptre = hash_rec(&ht,cstate) + len - 1;
/* See if the set contains an accept-state */
    ptr = cs_ptr-1;
    while (++ptr <= cs_ptre) if (fsaptr->is_accepting[*ptr]) {
      det->is_accepting[cstate] = TRUE;
      ct++;
      break;
    }
    if (subsets) {
      tmalloc(det->states->intlist[cstate],int,len+1);
      det->states->intlist[cstate][0]=len;
      n=0;
      ptr = cs_ptr-1;
      while (++ptr <= cs_ptre)
        det->states->intlist[cstate][++n] = *ptr;
    }
  }

  det->num_accepting = ct;
  if (ct==1 || ct != ns) {
    tmalloc(det->accepting,int,ct+1);
    ct = 0;
    for (i=1;i<=ns;i++) if (det->is_accepting[i])
      det->accepting[++ct] = i;
  }
  tfree(fsaptr->is_accepting);
  tfree(det->is_accepting);
  hash_clear(&ht);
  tfree(fsarow);

  if (destroy)
    fsa_clear(fsaptr);

/* Now read the transition table back in */
  tempfile = fopen(tempfilename,"r");
  compressed_transitions_read(det,tempfile);
  fclose(tempfile);

  unlink(tempfilename);

  return det;
}

fsa *
nfa_cdeterminize(fsaptr,op_table_type,destroy,tempfilename)
	fsa *fsaptr;
	storage_type op_table_type;
	boolean destroy;
	char *tempfilename;
/* Version of nfa_determinize for transtition tables stored compactly.
 * FOR THE MOMENT WE ASSUME NO EPSILON TRANSITIONS
 * The fsa *fsaptr must be an fsa with compact table.
 * The returned fsa accepts the same language but is deterministic.
 */
{
  if (kbm_print_level>=3)
    printf("    #Calling nfa_determinize.\n");
  if (fsaptr->states->size < MAXUSHORT)
    return nfa_cdeterminize_short(
                      fsaptr,op_table_type,destroy,tempfilename);
  else
    return nfa_cdeterminize_int(
                      fsaptr,op_table_type,destroy,tempfilename);
}

fsa *
nfa_cdeterminize_short(fsaptr,op_table_type,destroy,tempfilename)
	fsa *fsaptr;
	storage_type op_table_type;
	boolean destroy;
	char *tempfilename;
{
  int ngens, nssi, nsi, ns, *fsarow,
      nt, cstate, csi, im, i, g1, len, ct;
  unsigned int **table, *tableptr, *tableptre, g1shift;
  unsigned short *ht_ptr, *ht_chptr, *ht_ptrb, *ht_ptre,
                 *cs_ptr, *cs_ptre, *ptr;
  boolean dense_op;
  short_hash_table ht;
  fsa *det;
  FILE *tempfile, *fopen();

  if (kbm_print_level>=3)
    printf("    #Calling nfa_determinize_short.\n");

  tmalloc(det,fsa,1);
  fsa_init(det);
  srec_copy(det->alphabet,fsaptr->alphabet);
  det->flags[DFA] = TRUE;
  det->flags[ACCESSIBLE] = TRUE;
  det->flags[BFS] = TRUE;

  det->states->type = SIMPLE;

  det->table->table_type = op_table_type;
  det->table->denserows = 0;
  det->table->printing_format = op_table_type;

  if (fsaptr->num_initial==0) {
    det->num_initial = 0;
    det->num_accepting = 0;
    det->states->size = 0;
    if (destroy)
      fsa_clear(fsaptr);
    return det;
  }
  ngens = det->alphabet->size;
  nsi = fsaptr->states->size;

  fsa_set_is_accepting(fsaptr);

  dense_op = op_table_type==DENSE;
  table = fsaptr->table->ctable_data_ptr;

  det->num_initial = 1;
  tmalloc(det->initial,int,2);
  det->initial[1] = 1;
  
  short_hash_init(&ht,FALSE,0,0,0);
  ht_ptrb = ht.current_ptr;
  ht_ptre = ht_ptrb-1;
  nssi = fsaptr->num_initial;
  for (i=0;i<nssi;i++)
    *(++ht_ptre) = fsaptr->initial[i+1];
  im = short_hash_locate(&ht,ht_ptre-ht_ptrb+1);
/* Each state in 'det' will be represented as a subset of the set of states
 * of *fsaptr. The initial state contains the initial states
 * of *fsaptr.
 * A subset is an accept-state if it contains an accept state of *fsaptr
 * The subsets will be stored as variable-length records in the hash-table,
 * always in increasing order.
 */
  if (im!=1) {
    fprintf(stderr,"Hash-initialisation problem in nfa_determinize.\n");
    return 0;
  }
  if ((tempfile=fopen(tempfilename,"w"))==0){
    fprintf(stderr,"Error: cannot open file %s\n",tempfilename);
    return 0;
  }
  if (dense_op)
    tmalloc(fsarow,int,ngens)
  else
    tmalloc(fsarow,int,2*ngens+1)
 
  cstate = 0;
  if (dense_op)
    len = ngens; /* The length of the fsarow output. */
  nt = 0; /* Number of transitions in det */

  while (++cstate <= ht.num_recs) {
    if (kbm_print_level>=3) {
      if ((cstate<=1000 && cstate%100==0)||(cstate<=10000 && cstate%1000==0)||
          (cstate<=100000 && cstate%5000==0) || cstate%50000==0)
       printf("    #cstate = %d;  number of states = %d.\n",cstate,ht.num_recs);
    }
    cs_ptr = short_hash_rec(&ht,cstate);
    cs_ptre = short_hash_rec(&ht,cstate) + short_hash_rec_len(&ht,cstate) - 1;
    if (!dense_op)
      len = 0;

    for (g1=1;g1<=ngens;g1++) {
/* Calculate action of generator g1 on state cstate  - to get the image, we
 * simply apply it to each state in the subset of states representing cstate.
 */
      g1shift = ((unsigned)g1) << SHIFT;
      ht_ptrb = ht.current_ptr;
      ht_ptre = ht_ptrb-1;
      ptr = cs_ptr-1;
      while (++ptr <= cs_ptre) {
        tableptr=table[*ptr]; tableptre=table[*ptr+1]; 
        while (tableptr < tableptre){
          if ((*tableptr & MASKL) == g1shift) {
            csi = *tableptr & MASKR;
            if (csi==0)
              continue;
            if (ht_ptrb>ht_ptre || csi> *ht_ptre) {
    /* We have a new state for the image subset to be added to the end */
              *(++ht_ptre) = csi;
            }
            else {
              ht_chptr = ht_ptrb;
              while (*ht_chptr < csi)
                ht_chptr++;
              if (csi < *ht_chptr) {
    /* we have a new state for the image subset to be added in the middle */
                ht_ptr = ++ht_ptre;
                while (ht_ptr > ht_chptr) {
                  *ht_ptr = *(ht_ptr-1);
                  ht_ptr--;
                }
                *ht_ptr = csi;
              }
            }
          }
          tableptr++;
        }
      }
      im = short_hash_locate(&ht,ht_ptre-ht_ptrb+1);
      if (dense_op)
         fsarow[g1-1] = im;
      else if (im>0) {
         fsarow[++len] = g1;
         fsarow[++len] = im;
      }
      if (im>0)
        nt++;
    }
    if (!dense_op)
      fsarow[0] = len++;
    fwrite((void *)fsarow,sizeof(int),(size_t)len,tempfile);
  }
  fclose(tempfile);

  ns = det->states->size = ht.num_recs;
  det->table->numTransitions = nt;

/* Locate the accept states. A state is an accept state if and only if
 * the subset representing it contains an accept state of *fsaptr.
 */
  tmalloc(det->is_accepting,boolean,ns+1);
  for (i=1;i<=ns;i++)
    det->is_accepting[i] = FALSE;
  ct = 0;
  for (cstate=1;cstate<=ns;cstate++) {
    cs_ptr = short_hash_rec(&ht,cstate);
    cs_ptre = short_hash_rec(&ht,cstate) + short_hash_rec_len(&ht,cstate) - 1;
/* See if the set contains an accept-state */
    ptr = cs_ptr-1;
    while (++ptr <= cs_ptre) if (fsaptr->is_accepting[*ptr]) {
      det->is_accepting[cstate] = TRUE;
      ct++;
      break;
    }
  }

  det->num_accepting = ct;
  if (ct==1 || ct != ns) {
    tmalloc(det->accepting,int,ct+1);
    ct = 0;
    for (i=1;i<=ns;i++) if (det->is_accepting[i])
      det->accepting[++ct] = i;
  }
  tfree(fsaptr->is_accepting);
  tfree(det->is_accepting);
  short_hash_clear(&ht);
  tfree(fsarow);

  if (destroy)
    fsa_clear(fsaptr);

/* Now read the transition table back in */
  tempfile = fopen(tempfilename,"r");
  compressed_transitions_read(det,tempfile);
  fclose(tempfile);

  unlink(tempfilename);

  return det;
}

fsa *
nfa_cdeterminize_int(fsaptr,op_table_type,destroy,tempfilename)
	fsa *fsaptr;
	storage_type op_table_type;
	boolean destroy;
	char *tempfilename;
{
  int ngens, nssi, nsi, ns, *fsarow,
      nt, cstate, csi, im, i, g1, len, ct;
  unsigned int **table, *tableptr, *tableptre, g1shift;
  int *ht_ptr, *ht_chptr, *ht_ptrb, *ht_ptre,
                 *cs_ptr, *cs_ptre, *ptr;
  boolean dense_op;
  hash_table ht;
  fsa *det;
  FILE *tempfile, *fopen();

  if (kbm_print_level>=3)
    printf("    #Calling nfa_determinize_short.\n");

  tmalloc(det,fsa,1);
  fsa_init(det);
  srec_copy(det->alphabet,fsaptr->alphabet);
  det->flags[DFA] = TRUE;
  det->flags[ACCESSIBLE] = TRUE;
  det->flags[BFS] = TRUE;

  det->states->type = SIMPLE;

  det->table->table_type = op_table_type;
  det->table->denserows = 0;
  det->table->printing_format = op_table_type;

  if (fsaptr->num_initial==0) {
    det->num_initial = 0;
    det->num_accepting = 0;
    det->states->size = 0;
    if (destroy)
      fsa_clear(fsaptr);
    return det;
  }
  ngens = det->alphabet->size;
  nsi = fsaptr->states->size;

  fsa_set_is_accepting(fsaptr);

  dense_op = op_table_type==DENSE;
  table = fsaptr->table->ctable_data_ptr;

  det->num_initial = 1;
  tmalloc(det->initial,int,2);
  det->initial[1] = 1;
  
  hash_init(&ht,FALSE,0,0,0);
  ht_ptrb = ht.current_ptr;
  ht_ptre = ht_ptrb-1;
  nssi = fsaptr->num_initial;
  for (i=0;i<nssi;i++)
    *(++ht_ptre) = fsaptr->initial[i+1];
  im = hash_locate(&ht,ht_ptre-ht_ptrb+1);
/* Each state in 'det' will be represented as a subset of the set of states
 * of *fsaptr. The initial state contains the initial states
 * of *fsaptr.
 * A subset is an accept-state if it contains an accept state of *fsaptr
 * The subsets will be stored as variable-length records in the hash-table,
 * always in increasing order.
 */
  if (im!=1) {
    fprintf(stderr,"Hash-initialisation problem in nfa_determinize.\n");
    return 0;
  }
  if ((tempfile=fopen(tempfilename,"w"))==0){
    fprintf(stderr,"Error: cannot open file %s\n",tempfilename);
    return 0;
  }
  if (dense_op)
    tmalloc(fsarow,int,ngens)
  else
    tmalloc(fsarow,int,2*ngens+1)
 
  cstate = 0;
  if (dense_op)
    len = ngens; /* The length of the fsarow output. */
  nt = 0; /* Number of transitions in det */

  while (++cstate <= ht.num_recs) {
    if (kbm_print_level>=3) {
      if ((cstate<=1000 && cstate%100==0)||(cstate<=10000 && cstate%1000==0)||
          (cstate<=100000 && cstate%5000==0) || cstate%50000==0)
       printf("    #cstate = %d;  number of states = %d.\n",cstate,ht.num_recs);
    }
    cs_ptr = hash_rec(&ht,cstate);
    cs_ptre = hash_rec(&ht,cstate) + hash_rec_len(&ht,cstate) - 1;
    if (!dense_op)
      len = 0;

    for (g1=1;g1<=ngens;g1++) {
/* Calculate action of generator g1 on state cstate  - to get the image, we
 * simply apply it to each state in the subset of states representing cstate.
 */
      g1shift = ((unsigned)g1) << SHIFT;
      ht_ptrb = ht.current_ptr;
      ht_ptre = ht_ptrb-1;
      ptr = cs_ptr-1;
      while (++ptr <= cs_ptre) {
        tableptr=table[*ptr]; tableptre=table[*ptr+1]; 
        while (tableptr < tableptre){
          if ((*tableptr & MASKL) == g1shift) {
            csi = *tableptr & MASKR;
            if (csi==0)
              continue;
            if (ht_ptrb>ht_ptre || csi> *ht_ptre) {
    /* We have a new state for the image subset to be added to the end */
              *(++ht_ptre) = csi;
            }
            else {
              ht_chptr = ht_ptrb;
              while (*ht_chptr < csi)
                ht_chptr++;
              if (csi < *ht_chptr) {
    /* we have a new state for the image subset to be added in the middle */
                ht_ptr = ++ht_ptre;
                while (ht_ptr > ht_chptr) {
                  *ht_ptr = *(ht_ptr-1);
                  ht_ptr--;
                }
                *ht_ptr = csi;
              }
            }
          }
          tableptr++;
        }
      }
      im = hash_locate(&ht,ht_ptre-ht_ptrb+1);
      if (dense_op)
         fsarow[g1-1] = im;
      else if (im>0) {
         fsarow[++len] = g1;
         fsarow[++len] = im;
      }
      if (im>0)
        nt++;
    }
    if (!dense_op)
      fsarow[0] = len++;
    fwrite((void *)fsarow,sizeof(int),(size_t)len,tempfile);
  }
  fclose(tempfile);

  ns = det->states->size = ht.num_recs;
  det->table->numTransitions = nt;

/* Locate the accept states. A state is an accept state if and only if
 * the subset representing it contains an accept state of *fsaptr.
 */
  tmalloc(det->is_accepting,boolean,ns+1);
  for (i=1;i<=ns;i++)
    det->is_accepting[i] = FALSE;
  ct = 0;
  for (cstate=1;cstate<=ns;cstate++) {
    cs_ptr = hash_rec(&ht,cstate);
    cs_ptre = hash_rec(&ht,cstate) + hash_rec_len(&ht,cstate) - 1;
/* See if the set contains an accept-state */
    ptr = cs_ptr-1;
    while (++ptr <= cs_ptre) if (fsaptr->is_accepting[*ptr]) {
      det->is_accepting[cstate] = TRUE;
      ct++;
      break;
    }
  }

  det->num_accepting = ct;
  if (ct==1 || ct != ns) {
    tmalloc(det->accepting,int,ct+1);
    ct = 0;
    for (i=1;i<=ns;i++) if (det->is_accepting[i])
      det->accepting[++ct] = i;
  }
  tfree(fsaptr->is_accepting);
  tfree(det->is_accepting);
  hash_clear(&ht);
  tfree(fsarow);

  if (destroy)
    fsa_clear(fsaptr);

/* Now read the transition table back in */
  tempfile = fopen(tempfilename,"r");
  compressed_transitions_read(det,tempfile);
  fclose(tempfile);

  unlink(tempfilename);

  return det;
}

fsa *
nfa_exists(fsaptr,op_table_type,destroy,tempfilename)
	fsa *fsaptr;
	storage_type op_table_type;
	boolean destroy;
	char *tempfilename;
/* *fsaptr must be a 2-variable (non-deterministic) fsa.
 * For the moment we assume it has no epsilon transitions.
 * The returned fsa is deterministic and accepts a word w_1 iff (w_1,w_2) is
 * accepted by *fsaptr, for some w_2 (with the usual padding conventions).
 * In fact, nfa_exists calls nfa_exists_int or nfa_exists_short,
 * the latter using the short hash table functions.
 */
{
  if (kbm_print_level>=3)
    printf("    #Calling nfa_exists.\n");
  if (fsaptr->states->size < MAXUSHORT)
    return nfa_exists_short(fsaptr,op_table_type,destroy,tempfilename);
  else
    return nfa_exists_int(fsaptr,op_table_type,destroy,tempfilename);
}

fsa *
nfa_exists_short(fsaptr,op_table_type,destroy,tempfilename)
	fsa *fsaptr;
	storage_type op_table_type;
	boolean destroy;
	char *tempfilename;
{
  int **table, ne, *tableptr, *tableptre, ngens, nsi, ns, dr, *fsarow, e,
      es, ef, nt, cstate, cs, csi, im, i, k, g1, len, ct;
  unsigned short *ht_ptr, *ht_chptr, *ht_ptrb, *ht_ptre,
                 *cs_ptr, *cs_ptre, *ptr;
  boolean dense_ip, dense_op, got;
  short_hash_table ht;
  fsa *exists;
  FILE *tempfile, *fopen();

  if (kbm_print_level>=3)
    printf("    #Calling nfa_exists_short.\n");

  if (fsaptr->alphabet->type != PRODUCT || fsaptr->alphabet->arity != 2) {
    fprintf(stderr,"Error in nfa_exists: fsa must be 2-variable.\n");
    return 0;
  }

  tmalloc(exists,fsa,1);
  fsa_init(exists);
  srec_copy(exists->alphabet,fsaptr->alphabet->base);
  exists->flags[DFA] = TRUE;
  exists->flags[ACCESSIBLE] = TRUE;
  exists->flags[BFS] = TRUE;

  exists->states->type = SIMPLE;

  exists->table->table_type = op_table_type;
  exists->table->denserows = 0;
  exists->table->printing_format = op_table_type;

  if (fsaptr->num_initial==0) {
    exists->num_initial = 0;
    exists->num_accepting = 0;
    exists->states->size = 0;
    if (destroy)
      fsa_clear(fsaptr);
    return exists;
  }
  ne = fsaptr->alphabet->size;
  ngens = exists->alphabet->size;
  nsi = fsaptr->states->size;

  if (ne != (ngens+1)*(ngens+1)-1) {
   fprintf(stderr,
     "Error: in a 2-variable fsa, alphabet size should = (ngens+1)^2 - 1.\n");
    return 0;
  }

  fsa_set_is_accepting(fsaptr);

  dense_ip = fsaptr->table->table_type==DENSE;
  dr = fsaptr->table->denserows;
  dense_op = op_table_type==DENSE;
  table = fsaptr->table->table_data_ptr;

  exists->num_initial = 1;
  tmalloc(exists->initial,int,2);
  exists->initial[1] = 1;
  
  short_hash_init(&ht,FALSE,0,0,0);
  ht_ptr = ht.current_ptr;
  k=fsaptr->num_initial;
  for (i=1;i<=k;i++)
    ht_ptr[i-1] = fsaptr->initial[i];
  im = short_hash_locate(&ht,k);
/* Each state in 'exists' will be represented as a subset of the set of states
 * of *fsaptr. The initial state consists of the initial states
 * of *fsaptr. A subset is an accept-state if it contains an accept state of
 * *fsaptr, or if one can get to an accept-state by applying elements
 * ($,x) where $ is the padding symbol.
 * The subsets will be stored as variable-length records in the hash-table,
 * always in increasing order.
 */
  if (im!=1) {
    fprintf(stderr,"Hash-initialisation problem in nfa_exists.\n");
    return 0;
  }
  if ((tempfile=fopen(tempfilename,"w"))==0){
    fprintf(stderr,"Error: cannot open file %s\n",tempfilename);
    return 0;
  }
  if (dense_op)
    tmalloc(fsarow,int,ngens)
  else
    tmalloc(fsarow,int,2*ngens+1)
 
  cstate = 0;
  if (dense_op)
    len = ngens; /* The length of the fsarow output. */
  nt = 0; /* Number of transitions in exists */

  while (++cstate <= ht.num_recs) {
    if (kbm_print_level>=3) {
      if ((cstate<=1000 && cstate%100==0)||(cstate<=10000 && cstate%1000==0)||
          (cstate<=100000 && cstate%5000==0) || cstate%50000==0)
       printf("    #cstate = %d;  number of states = %d.\n",cstate,ht.num_recs);
    }
    cs_ptr = short_hash_rec(&ht,cstate);
    cs_ptre = short_hash_rec(&ht,cstate) + short_hash_rec_len(&ht,cstate) - 1;
    if (!dense_op)
      len = 0;

    for (g1=1;g1<=ngens;g1++) {
/* Calculate action of generator g1 on state cstate  - to get the image, we
 * have to apply (g1,g2) to each element in the subset corresponding to cstate,
 * and this for each generator g2 of the base-alphabet (including the padding
 * symbol).
 */
      ht_ptrb = ht.current_ptr;
      ht_ptre = ht_ptrb-1;
      ptr = cs_ptr-1;
      es = (g1-1)*(ngens+1) + 1;
      ef = g1*(ngens+1);
/* As g2 ranges from 1 to ngens+1 in the pair (g1,g2), for fixed g1, the
 * corresponding edge number in the fsa ranges from es to ef.
 */
      while (++ptr <= cs_ptre) {
        tableptr=table[*ptr]; tableptre=table[*ptr+1]; 
        while (tableptr < tableptre){
          if (*tableptr>=es && *tableptr<=ef) {
            csi = *(tableptr+1);
            if (csi==0)
              continue;
            if (ht_ptrb>ht_ptre || csi> *ht_ptre) {
/* We have a new state for the image subset to be added to the end */
              *(++ht_ptre) = csi;
            }
            else {
              ht_chptr = ht_ptrb;
              while (*ht_chptr < csi)
                ht_chptr++;
              if (csi < *ht_chptr) {
/* we have a new state for the image subset to be added in the middle */
                ht_ptr = ++ht_ptre;
                while (ht_ptr > ht_chptr) {
                  *ht_ptr = *(ht_ptr-1);
                  ht_ptr--;
                }
                *ht_ptr = csi;
              }
            }
          }
          tableptr+=2;
        }
      }
      im = short_hash_locate(&ht,ht_ptre-ht_ptrb+1);
      if (dense_op)
         fsarow[g1-1] = im;
      else if (im>0) {
         fsarow[++len] = g1;
         fsarow[++len] = im;
      }
      if (im>0)
        nt++;
    }
    if (!dense_op)
      fsarow[0] = len++;
    fwrite((void *)fsarow,sizeof(int),(size_t)len,tempfile);
  }
  fclose(tempfile);

  ns = exists->states->size = ht.num_recs;
  exists->table->numTransitions = nt;

/* Locate the accept states. This is slightly cumbersome, since a state
 * is an accept state if either the corresponding subset contains an
 * accept state of *fsaptr, or we can get from some such state to an
 * accept state by applying elements ($,x).
 * We will need to use the array exists->is_accepting.
 */
  tmalloc(exists->is_accepting,boolean,ns+1);
  for (i=1;i<=ns;i++)
    exists->is_accepting[i] = FALSE;
  ct = 0;
  for (cstate=ns;cstate>=1;cstate--) {
/* We work backwards through the states, since we wish to add on additional
 * elements at the end of the list in the hash-table - this destroys
 * later entries, but that doesn't matter, since we have already dealt
 * with them.
 */
    cs_ptr = short_hash_rec(&ht,cstate);
    cs_ptre = short_hash_rec(&ht,cstate) + short_hash_rec_len(&ht,cstate) - 1;
/* First see if the set itself contains an accept-state */
    ptr = cs_ptr-1;
    while (++ptr <= cs_ptre) if (fsaptr->is_accepting[*ptr]) {
      exists->is_accepting[cstate] = TRUE;
      ct++;
      break;
    }
    if (exists->is_accepting[cstate])
      continue;
/* Next apply generators ($,x) and see if we get anything new, and
 * if it is an accept state.
 * Anything new is added to the end of the list - we don't need to
 * bother about having them in increasing order this time.
 */
    es = ngens*(ngens+1)+1;
    ef = (ngens+1)*(ngens+1)-1;
    ptr = cs_ptr-1;
    while (++ptr <= cs_ptre) {
      tableptr=table[*ptr]; tableptre=table[*ptr+1]; 
      while (tableptr < tableptre){
        if (*tableptr>=es && *tableptr<=ef) {
          csi = *(tableptr+1);
          if (csi==0)
            continue;
          if (fsaptr->is_accepting[csi]) {
            exists->is_accepting[cstate] = TRUE;
            ct++;
            break;
          }
/* see if csi is new */
          ht_chptr = cs_ptr-1;
          got = FALSE;
          while (++ht_chptr <= cs_ptre) if (csi == *ht_chptr) {
            got = TRUE;
            break;
          }
          if (!got) 
/* add csi to the end */
            *(++cs_ptre) = csi;
        }
        tableptr+=2;
      }
      if (exists->is_accepting[cstate])
        break;
    }
  }

  exists->num_accepting = ct;
  if (ct==1 || ct != ns) {
    tmalloc(exists->accepting,int,ct+1);
    ct = 0;
    for (i=1;i<=ns;i++) if (exists->is_accepting[i])
      exists->accepting[++ct] = i;
  }
  tfree(fsaptr->is_accepting);
  tfree(exists->is_accepting);
  short_hash_clear(&ht);
  tfree(fsarow);

  if (destroy)
    fsa_clear(fsaptr);

/* Now read the transition table back in */
  tempfile = fopen(tempfilename,"r");
  compressed_transitions_read(exists,tempfile);
  fclose(tempfile);

  unlink(tempfilename);

  return exists;
}

fsa *
nfa_exists_int(fsaptr,op_table_type,destroy,tempfilename)
	fsa *fsaptr;
	storage_type op_table_type;
	boolean destroy;
	char *tempfilename;
{
  int **table, ne, *tableptr, *tableptre, ngens, nsi, ns, dr, *fsarow, e,
      es, ef, nt, cstate, cs, csi, im, i, k, g1, len, ct;
  int *ht_ptr, *ht_chptr, *ht_ptrb, *ht_ptre,
                 *cs_ptr, *cs_ptre, *ptr;
  boolean dense_ip, dense_op, got;
  hash_table ht;
  fsa *exists;
  FILE *tempfile, *fopen();

  if (kbm_print_level>=3)
    printf("    #Calling nfa_exists_int.\n");

  if (fsaptr->alphabet->type != PRODUCT || fsaptr->alphabet->arity != 2) {
    fprintf(stderr,"Error in nfa_exists: fsa must be 2-variable.\n");
    return 0;
  }

  tmalloc(exists,fsa,1);
  fsa_init(exists);
  srec_copy(exists->alphabet,fsaptr->alphabet->base);
  exists->flags[DFA] = TRUE;
  exists->flags[ACCESSIBLE] = TRUE;
  exists->flags[BFS] = TRUE;

  exists->states->type = SIMPLE;

  exists->table->table_type = op_table_type;
  exists->table->denserows = 0;
  exists->table->printing_format = op_table_type;

  if (fsaptr->num_initial==0) {
    exists->num_initial = 0;
    exists->num_accepting = 0;
    exists->states->size = 0;
    if (destroy)
      fsa_clear(fsaptr);
    return exists;
  }
  ne = fsaptr->alphabet->size;
  ngens = exists->alphabet->size;
  nsi = fsaptr->states->size;

  if (ne != (ngens+1)*(ngens+1)-1) {
   fprintf(stderr,
     "Error: in a 2-variable fsa, alphabet size should = (ngens+1)^2 - 1.\n");
    return 0;
  }

  fsa_set_is_accepting(fsaptr);

  dense_ip = fsaptr->table->table_type==DENSE;
  dr = fsaptr->table->denserows;
  dense_op = op_table_type==DENSE;
  table = fsaptr->table->table_data_ptr;

  exists->num_initial = 1;
  tmalloc(exists->initial,int,2);
  exists->initial[1] = 1;
  
  hash_init(&ht,FALSE,0,0,0);
  ht_ptr = ht.current_ptr;
  k=fsaptr->num_initial;
  for (i=1;i<=k;i++)
    ht_ptr[i-1] = fsaptr->initial[i];
  im = hash_locate(&ht,k);
/* Each state in 'exists' will be represented as a subset of the set of states
 * of *fsaptr. The initial state consists of the initial states
 * of *fsaptr. A subset is an accept-state if it contains an accept state of
 * *fsaptr, or if one can get to an accept-state by applying elements
 * ($,x) where $ is the padding symbol.
 * The subsets will be stored as variable-length records in the hash-table,
 * always in increasing order.
 */
  if (im!=1) {
    fprintf(stderr,"Hash-initialisation problem in nfa_exists.\n");
    return 0;
  }
  if ((tempfile=fopen(tempfilename,"w"))==0){
    fprintf(stderr,"Error: cannot open file %s\n",tempfilename);
    return 0;
  }
  if (dense_op)
    tmalloc(fsarow,int,ngens)
  else
    tmalloc(fsarow,int,2*ngens+1)
 
  cstate = 0;
  if (dense_op)
    len = ngens; /* The length of the fsarow output. */
  nt = 0; /* Number of transitions in exists */

  while (++cstate <= ht.num_recs) {
    if (kbm_print_level>=3) {
      if ((cstate<=1000 && cstate%100==0)||(cstate<=10000 && cstate%1000==0)||
          (cstate<=100000 && cstate%5000==0) || cstate%50000==0)
       printf("    #cstate = %d;  number of states = %d.\n",cstate,ht.num_recs);
    }
    cs_ptr = hash_rec(&ht,cstate);
    cs_ptre = hash_rec(&ht,cstate) + hash_rec_len(&ht,cstate) - 1;
    if (!dense_op)
      len = 0;

    for (g1=1;g1<=ngens;g1++) {
/* Calculate action of generator g1 on state cstate  - to get the image, we
 * have to apply (g1,g2) to each element in the subset corresponding to cstate,
 * and this for each generator g2 of the base-alphabet (including the padding
 * symbol).
 */
      ht_ptrb = ht.current_ptr;
      ht_ptre = ht_ptrb-1;
      ptr = cs_ptr-1;
      es = (g1-1)*(ngens+1) + 1;
      ef = g1*(ngens+1);
/* As g2 ranges from 1 to ngens+1 in the pair (g1,g2), for fixed g1, the
 * corresponding edge number in the fsa ranges from es to ef.
 */
      while (++ptr <= cs_ptre) {
        tableptr=table[*ptr]; tableptre=table[*ptr+1]; 
        while (tableptr < tableptre){
          if (*tableptr>=es && *tableptr<=ef) {
            csi = *(tableptr+1);
            if (csi==0)
              continue;
            if (ht_ptrb>ht_ptre || csi> *ht_ptre) {
/* We have a new state for the image subset to be added to the end */
              *(++ht_ptre) = csi;
            }
            else {
              ht_chptr = ht_ptrb;
              while (*ht_chptr < csi)
                ht_chptr++;
              if (csi < *ht_chptr) {
/* we have a new state for the image subset to be added in the middle */
                ht_ptr = ++ht_ptre;
                while (ht_ptr > ht_chptr) {
                  *ht_ptr = *(ht_ptr-1);
                  ht_ptr--;
                }
                *ht_ptr = csi;
              }
            }
          }
          tableptr+=2;
        }
      }
      im = hash_locate(&ht,ht_ptre-ht_ptrb+1);
      if (dense_op)
         fsarow[g1-1] = im;
      else if (im>0) {
         fsarow[++len] = g1;
         fsarow[++len] = im;
      }
      if (im>0)
        nt++;
    }
    if (!dense_op)
      fsarow[0] = len++;
    fwrite((void *)fsarow,sizeof(int),(size_t)len,tempfile);
  }
  fclose(tempfile);

  ns = exists->states->size = ht.num_recs;
  exists->table->numTransitions = nt;

/* Locate the accept states. This is slightly cumbersome, since a state
 * is an accept state if either the corresponding subset contains an
 * accept state of *fsaptr, or we can get from some such state to an
 * accept state by applying elements ($,x).
 * We will need to use the array exists->is_accepting.
 */
  tmalloc(exists->is_accepting,boolean,ns+1);
  for (i=1;i<=ns;i++)
    exists->is_accepting[i] = FALSE;
  ct = 0;
  for (cstate=ns;cstate>=1;cstate--) {
/* We work backwards through the states, since we wish to add on additional
 * elements at the end of the list in the hash-table - this destroys
 * later entries, but that doesn't matter, since we have already dealt
 * with them.
 */
    cs_ptr = hash_rec(&ht,cstate);
    cs_ptre = hash_rec(&ht,cstate) + hash_rec_len(&ht,cstate) - 1;
/* First see if the set itself contains an accept-state */
    ptr = cs_ptr-1;
    while (++ptr <= cs_ptre) if (fsaptr->is_accepting[*ptr]) {
      exists->is_accepting[cstate] = TRUE;
      ct++;
      break;
    }
    if (exists->is_accepting[cstate])
      continue;
/* Next apply generators ($,x) and see if we get anything new, and
 * if it is an accept state.
 * Anything new is added to the end of the list - we don't need to
 * bother about having them in increasing order this time.
 */
    es = ngens*(ngens+1)+1;
    ef = (ngens+1)*(ngens+1)-1;
    ptr = cs_ptr-1;
    while (++ptr <= cs_ptre) {
      tableptr=table[*ptr]; tableptre=table[*ptr+1]; 
      while (tableptr < tableptre){
        if (*tableptr>=es && *tableptr<=ef) {
          csi = *(tableptr+1);
          if (csi==0)
            continue;
          if (fsaptr->is_accepting[csi]) {
            exists->is_accepting[cstate] = TRUE;
            ct++;
            break;
          }
/* see if csi is new */
          ht_chptr = cs_ptr-1;
          got = FALSE;
          while (++ht_chptr <= cs_ptre) if (csi == *ht_chptr) {
            got = TRUE;
            break;
          }
          if (!got) 
/* add csi to the end */
            *(++cs_ptre) = csi;
        }
        tableptr+=2;
      }
      if (exists->is_accepting[cstate])
        break;
    }
  }

  exists->num_accepting = ct;
  if (ct==1 || ct != ns) {
    tmalloc(exists->accepting,int,ct+1);
    ct = 0;
    for (i=1;i<=ns;i++) if (exists->is_accepting[i])
      exists->accepting[++ct] = i;
  }
  tfree(fsaptr->is_accepting);
  tfree(exists->is_accepting);
  hash_clear(&ht);
  tfree(fsarow);

  if (destroy)
    fsa_clear(fsaptr);

/* Now read the transition table back in */
  tempfile = fopen(tempfilename,"r");
  compressed_transitions_read(exists,tempfile);
  fclose(tempfile);

  unlink(tempfilename);

  return exists;
}
