Node *
right_linked(Node *n)
{
if (!n) return n;
if (n->ntyp == AND || n->ntyp == OR)
while (n->lft && n->lft->ntyp == n->ntyp)
{ Node *tmp = n->lft;
n->lft = tmp->rgt;
tmp->rgt = n;
n = tmp;
}
n->lft = right_linked(n->lft);
n->rgt = right_linked(n->rgt);
return n;
}
static void
mk_red(Node *n)
{ Graph *p;
n = right_linked(n);
for (p = Nodes_Set; p; p = p->nxt)
{ if (p->outgoing
&& has_clause(0, p, n))
{ if (p->redcnt >= 63)
Fatal("too many Untils", (char *)0);
p->isred[p->redcnt++] =
(unsigned char) Red_cnt;
Lab_cnt++; Max_Red = Red_cnt;
} }
}
static void
mk_grn(Node *n)
{ Graph *p;
n = right_linked(n);
more:
for (p = Nodes_Set; p; p = p->nxt)
if (p->outgoing
&& has_clause(AND, p, n))
{ p->isgrn[p->grncnt++] =
(unsigned char) Red_cnt;
Lab_cnt++;
}
if (n->ntyp == U_OPER) /* 3.4.0 */
{ n = n->rgt;
goto more;
}
}
static int
has_clause(int tok, Graph *p, Node *n)
{ Node *q, *qq;
switch (n->ntyp) {
case AND:
return has_clause(tok, p, n->lft) &&
has_clause(tok, p, n->rgt);
case OR:
return has_clause(tok, p, n->lft) ||
has_clause(tok, p, n->rgt);
}
for (q = p->Other; q; q = q->nxt)
{ qq = right_linked(q);
if (anywhere(tok, n, qq))
return 1;
}
return 0;
}
static Node *bin_simpler(Node *ptr, Miscellaneous *miscell, int *cnt, char *uform, int *tl_yychar)
{ Node *a, *b;
if (ptr)
switch (ptr->ntyp) {
case U_OPER:
if (ptr->rgt->ntyp == TRUE
|| ptr->rgt->ntyp == FALSE
|| ptr->lft->ntyp == FALSE)
{ ptr = ptr->rgt;
break;
}
if (implies(ptr->lft, ptr->rgt, cnt, uform, tl_yychar, miscell)) /* NEW */
{ ptr = ptr->rgt;
break;
}
if (ptr->lft->ntyp == U_OPER
&& isequal(ptr->lft->lft, ptr->rgt, cnt, uform, tl_yychar, miscell))
{ /* (p U q) U p = (q U p) */
ptr->lft = ptr->lft->rgt;
break;
}
if (ptr->rgt->ntyp == U_OPER
&& implies(ptr->lft, ptr->rgt->lft, cnt, uform, tl_yychar, miscell))
{ /* NEW */
ptr = ptr->rgt;
break;
}
/* X p U X q == X (p U q) */
if (ptr->rgt->ntyp == NEXT
&& ptr->lft->ntyp == NEXT)
{ ptr = tl_nn(NEXT,
tl_nn(U_OPER,
ptr->lft->lft,
ptr->rgt->lft, miscell), ZN, miscell);
break;
}
/* NEW : F X p == X F p */
if (ptr->lft->ntyp == TRUE &&
ptr->rgt->ntyp == NEXT) {
ptr = tl_nn(NEXT, tl_nn(U_OPER, True, ptr->rgt->lft, miscell), ZN, miscell);
break;
}
/* NEW : F G F p == G F p */
if (ptr->lft->ntyp == TRUE &&
ptr->rgt->ntyp == V_OPER &&
ptr->rgt->lft->ntyp == FALSE &&
ptr->rgt->rgt->ntyp == U_OPER &&
ptr->rgt->rgt->lft->ntyp == TRUE) {
ptr = ptr->rgt;
break;
}
/* NEW */
if (ptr->lft->ntyp != TRUE &&
implies(push_negation(tl_nn(NOT, dupnode(ptr->rgt), ZN, miscell), miscell, cnt, uform, tl_yychar), ptr->lft, cnt, uform, tl_yychar, miscell))
{ ptr->lft = True;
break;
}
break;
case V_OPER:
if (ptr->rgt->ntyp == FALSE
|| ptr->rgt->ntyp == TRUE
|| ptr->lft->ntyp == TRUE)
{ ptr = ptr->rgt;
break;
}
if (implies(ptr->rgt, ptr->lft, cnt, uform, tl_yychar, miscell))
{ /* p V p = p */
ptr = ptr->rgt;
break;
}
/* F V (p V q) == F V q */
if (ptr->lft->ntyp == FALSE
&& ptr->rgt->ntyp == V_OPER)
{ ptr->rgt = ptr->rgt->rgt;
break;
}
/* NEW : G X p == X G p */
if (ptr->lft->ntyp == FALSE &&
ptr->rgt->ntyp == NEXT) {
ptr = tl_nn(NEXT, tl_nn(V_OPER, False, ptr->rgt->lft, miscell), ZN, miscell);
break;
}
/* NEW : G F G p == F G p */
if (ptr->lft->ntyp == FALSE &&
ptr->rgt->ntyp == U_OPER &&
ptr->rgt->lft->ntyp == TRUE &&
ptr->rgt->rgt->ntyp == V_OPER &&
ptr->rgt->rgt->lft->ntyp == FALSE) {
ptr = ptr->rgt;
break;
}
/* NEW */
if (ptr->rgt->ntyp == V_OPER
&& implies(ptr->rgt->lft, ptr->lft, cnt, uform, tl_yychar, miscell))
{ ptr = ptr->rgt;
break;
}
/* NEW */
if (ptr->lft->ntyp != FALSE &&
implies(ptr->lft,
push_negation(tl_nn(NOT, dupnode(ptr->rgt), ZN, miscell), miscell, cnt, uform, tl_yychar), cnt, uform, tl_yychar, miscell))
{ ptr->lft = False;
break;
}
break;
case NEXT:
/* NEW : X G F p == G F p */
if (ptr->lft->ntyp == V_OPER &&
ptr->lft->lft->ntyp == FALSE &&
ptr->lft->rgt->ntyp == U_OPER &&
ptr->lft->rgt->lft->ntyp == TRUE) {
break;
}
/* NEW : X F G p == F G p */
if (ptr->lft->ntyp == U_OPER &&
ptr->lft->lft->ntyp == TRUE &&
ptr->lft->rgt->ntyp == V_OPER &&
ptr->lft->rgt->lft->ntyp == FALSE) {
break;
}
break;
case ALWAYS:
/* NEW : [] G F p == G F p */
if (ptr->rgt->ntyp == V_OPER &&
ptr->rgt->rgt->ntyp == FALSE &&
ptr->rgt->lft->ntyp == U_OPER &&
ptr->rgt->lft->rgt->ntyp == TRUE) {
ptr = ptr->rgt;
break;
}
/* NEW : [] F G p == F G p */
if (ptr->rgt->ntyp == U_OPER &&
ptr->rgt->rgt->ntyp == TRUE &&
ptr->rgt->lft->ntyp == V_OPER &&
ptr->rgt->lft->rgt->ntyp == FALSE) {
ptr = ptr->rgt;
break;
}
break;
case IMPLIES:
if (implies(ptr->lft, ptr->rgt, cnt, uform, tl_yychar, miscell))
{ ptr = True;
break;
}
ptr = tl_nn(OR, Not(ptr->lft), ptr->rgt, miscell);
ptr = canonical(right_linked(ptr), miscell, cnt, uform, tl_yychar);
break;
case EQUIV:
if (implies(ptr->lft, ptr->rgt, cnt, uform, tl_yychar, miscell) &&
implies(ptr->rgt, ptr->lft, cnt, uform, tl_yychar, miscell))
{ ptr = True;
break;
}
a = canonical(right_linked(tl_nn(AND,
dupnode(ptr->lft),
dupnode(ptr->rgt), miscell)), miscell, cnt, uform, tl_yychar);
b = canonical(right_linked(tl_nn(AND,
Not(ptr->lft),
Not(ptr->rgt), miscell)), miscell, cnt, uform, tl_yychar);
ptr = tl_nn(OR, a, b, miscell);
ptr = canonical(right_linked(ptr), miscell, cnt, uform, tl_yychar);
break;
case AND:
/* p && (q U p) = p */
if (ptr->rgt->ntyp == U_OPER
&& isequal(ptr->rgt->rgt, ptr->lft, cnt, uform, tl_yychar, miscell))
{ ptr = ptr->lft;
break;
}
if (ptr->lft->ntyp == U_OPER
&& isequal(ptr->lft->rgt, ptr->rgt, cnt, uform, tl_yychar, miscell))
{ ptr = ptr->rgt;
break;
}
/* p && (q V p) == q V p */
if (ptr->rgt->ntyp == V_OPER
&& isequal(ptr->rgt->rgt, ptr->lft, cnt, uform, tl_yychar, miscell))
{ ptr = ptr->rgt;
break;
}
if (ptr->lft->ntyp == V_OPER
&& isequal(ptr->lft->rgt, ptr->rgt, cnt, uform, tl_yychar, miscell))
{ ptr = ptr->lft;
break;
}
/* (p U q) && (r U q) = (p && r) U q*/
if (ptr->rgt->ntyp == U_OPER
&& ptr->lft->ntyp == U_OPER
&& isequal(ptr->rgt->rgt, ptr->lft->rgt, cnt, uform, tl_yychar, miscell))
{ ptr = tl_nn(U_OPER,
tl_nn(AND, ptr->lft->lft, ptr->rgt->lft, miscell),
ptr->lft->rgt, miscell);
break;
}
/* (p V q) && (p V r) = p V (q && r) */
if (ptr->rgt->ntyp == V_OPER
&& ptr->lft->ntyp == V_OPER
&& isequal(ptr->rgt->lft, ptr->lft->lft, cnt, uform, tl_yychar, miscell))
{ ptr = tl_nn(V_OPER,
ptr->rgt->lft,
tl_nn(AND, ptr->lft->rgt, ptr->rgt->rgt, miscell), miscell);
break;
}
/* X p && X q == X (p && q) */
if (ptr->rgt->ntyp == NEXT
&& ptr->lft->ntyp == NEXT)
{ ptr = tl_nn(NEXT,
tl_nn(AND,
ptr->rgt->lft,
ptr->lft->lft, miscell), ZN, miscell);
break;
}
/* (p V q) && (r U q) == p V q */
if (ptr->rgt->ntyp == U_OPER
&& ptr->lft->ntyp == V_OPER
&& isequal(ptr->lft->rgt, ptr->rgt->rgt, cnt, uform, tl_yychar, miscell))
{ ptr = ptr->lft;
break;
}
if (isequal(ptr->lft, ptr->rgt, cnt, uform, tl_yychar, miscell) /* (p && p) == p */
|| ptr->rgt->ntyp == FALSE /* (p && F) == F */
|| ptr->lft->ntyp == TRUE /* (T && p) == p */
|| implies(ptr->rgt, ptr->lft, cnt, uform, tl_yychar, miscell))/* NEW */
{ ptr = ptr->rgt;
break;
}
if (ptr->rgt->ntyp == TRUE /* (p && T) == p */
|| ptr->lft->ntyp == FALSE /* (F && p) == F */
|| implies(ptr->lft, ptr->rgt, cnt, uform, tl_yychar, miscell))/* NEW */
{ ptr = ptr->lft;
break;
}
/* NEW : F G p && F G q == F G (p && q) */
if (ptr->lft->ntyp == U_OPER &&
ptr->lft->lft->ntyp == TRUE &&
ptr->lft->rgt->ntyp == V_OPER &&
ptr->lft->rgt->lft->ntyp == FALSE &&
ptr->rgt->ntyp == U_OPER &&
ptr->rgt->lft->ntyp == TRUE &&
ptr->rgt->rgt->ntyp == V_OPER &&
ptr->rgt->rgt->lft->ntyp == FALSE)
{
ptr = tl_nn(U_OPER, True,
tl_nn(V_OPER, False,
tl_nn(AND, ptr->lft->rgt->rgt,
ptr->rgt->rgt->rgt, miscell), miscell), miscell);
break;
}
/* NEW */
if (implies(ptr->lft,
push_negation(tl_nn(NOT, dupnode(ptr->rgt), ZN, miscell), miscell, cnt, uform, tl_yychar), cnt, uform, tl_yychar, miscell)
|| implies(ptr->rgt,
push_negation(tl_nn(NOT, dupnode(ptr->lft), ZN, miscell), miscell, cnt, uform, tl_yychar), cnt, uform, tl_yychar, miscell))
{ ptr = False;
break;
}
break;
case OR:
/* p || (q U p) == q U p */
if (ptr->rgt->ntyp == U_OPER
&& isequal(ptr->rgt->rgt, ptr->lft, cnt, uform, tl_yychar, miscell))
{ ptr = ptr->rgt;
break;
}
/* p || (q V p) == p */
if (ptr->rgt->ntyp == V_OPER
&& isequal(ptr->rgt->rgt, ptr->lft, cnt, uform, tl_yychar, miscell))
{ ptr = ptr->lft;
break;
}
/* (p U q) || (p U r) = p U (q || r) */
if (ptr->rgt->ntyp == U_OPER
&& ptr->lft->ntyp == U_OPER
&& isequal(ptr->rgt->lft, ptr->lft->lft, cnt, uform, tl_yychar, miscell))
{ ptr = tl_nn(U_OPER,
ptr->rgt->lft,
tl_nn(OR, ptr->lft->rgt, ptr->rgt->rgt, miscell), miscell);
break;
}
if (isequal(ptr->lft, ptr->rgt, cnt, uform, tl_yychar, miscell) /* (p || p) == p */
|| ptr->rgt->ntyp == FALSE /* (p || F) == p */
|| ptr->lft->ntyp == TRUE /* (T || p) == T */
|| implies(ptr->rgt, ptr->lft, cnt, uform, tl_yychar, miscell))/* NEW */
{ ptr = ptr->lft;
break;
}
if (ptr->rgt->ntyp == TRUE /* (p || T) == T */
|| ptr->lft->ntyp == FALSE /* (F || p) == p */
|| implies(ptr->lft, ptr->rgt, cnt, uform, tl_yychar, miscell))/* NEW */
{ ptr = ptr->rgt;
break;
}
/* (p V q) || (r V q) = (p || r) V q */
if (ptr->rgt->ntyp == V_OPER
&& ptr->lft->ntyp == V_OPER
&& isequal(ptr->lft->rgt, ptr->rgt->rgt, cnt, uform, tl_yychar, miscell))
{ ptr = tl_nn(V_OPER,
tl_nn(OR, ptr->lft->lft, ptr->rgt->lft, miscell),
ptr->rgt->rgt, miscell);
break;
}
/* (p V q) || (r U q) == r U q */
if (ptr->rgt->ntyp == U_OPER
&& ptr->lft->ntyp == V_OPER
&& isequal(ptr->lft->rgt, ptr->rgt->rgt, cnt, uform, tl_yychar, miscell))
{ ptr = ptr->rgt;
break;
}
/* NEW : G F p || G F q == G F (p || q) */
if (ptr->lft->ntyp == V_OPER &&
ptr->lft->lft->ntyp == FALSE &&
ptr->lft->rgt->ntyp == U_OPER &&
ptr->lft->rgt->lft->ntyp == TRUE &&
ptr->rgt->ntyp == V_OPER &&
ptr->rgt->lft->ntyp == FALSE &&
ptr->rgt->rgt->ntyp == U_OPER &&
ptr->rgt->rgt->lft->ntyp == TRUE)
{
ptr = tl_nn(V_OPER, False,
tl_nn(U_OPER, True,
tl_nn(OR, ptr->lft->rgt->rgt,
ptr->rgt->rgt->rgt, miscell), miscell), miscell);
break;
}
/* NEW */
if (implies(push_negation(tl_nn(NOT, dupnode(ptr->rgt), ZN, miscell), miscell, cnt, uform, tl_yychar),
ptr->lft, cnt, uform, tl_yychar, miscell)
|| implies(push_negation(tl_nn(NOT, dupnode(ptr->lft), ZN, miscell), miscell, cnt, uform, tl_yychar),
ptr->rgt, cnt, uform, tl_yychar, miscell))
{ ptr = True;
break;
}
break;
}
return ptr;
}
