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WIP seq_split: derivative-based complement split (NOT for merge - soundness bug)

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Prototype of the notes.md redesign: Split(~a) for star-free a via r = E(~a) | RE(LF(delta(~a))) using brz_derivative_cofactors, of_pred(lambda) char-classes, per-iterator memo (threaded through head_normalize) + De Morgan fallback at ~(R*)/cyclic revisit.

RESULT: De Morgan split blow-up ELIMINATED (L15: complement/max-split-set 65536 -> 0), validating the core idea. BUT: (1) SOUNDNESS BUG - concat membership over a derivative-split complement returns spurious unsat ((x.y) in ~([0-9]^2): default sat, nseq unsat; single-var x in ~([0-9]^2) is correct). Split-set not collapsed (49 splits) so of_pred not empty-dropped; fault is downstream handling of of_pred(lambda) char-classes in the concat split/primitive path. (2) bottleneck moved to DFS nodes (7 -> 33071). FIX DIRECTION: represent the cofactor char-class as range/union-of-ranges nseq fully supports, not of_pred(lambda). Do not build on this until fixed.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
This commit is contained in:
Margus Veanes 2026-07-03 22:33:29 +03:00
parent 07c797c32b
commit 22eb098cd9
2 changed files with 52 additions and 11 deletions
Download patch file Download diff file Expand all files Collapse all files

50
src/ast/rewriter/seq_split.cpp
View file

@ -265,7 +265,16 @@ bool seq_split::complement(sort* seq_sort, split_set const& sp, split_set& resul
// emits *suspended* split-algebra terms (from_re / lcat / rcat / inter / compl) for
// the subterms instead of recursing. `mode` is irrelevant here: weak vs. strong is
// decided when `head_normalize` reaches an inter / compl node.
expr_ref seq_split::expand_fromre(expr* r, bool& ok) {
// Single-character regex for a cofactor path condition `pred` (a Boolean over the
// character (:var 0)): of_pred(lambda (c) . pred).
expr_ref seq_split::mk_charclass_re(expr* pred) {
sort* cs = seq().mk_char_sort();
symbol nm("c");
expr_ref lam(m.mk_lambda(1, &cs, &nm, pred), m);
return expr_ref(re().mk_of_pred(lam), m);
}
expr_ref seq_split::expand_fromre(expr* r, bool& ok, obj_hashtable<expr>& deriv_memo) {
ok = true;
++m_stats.m_sigma_expand;
seq_util& sq = seq();
@ -410,8 +419,30 @@ expr_ref seq_split::expand_fromre(expr* r, bool& ok) {
}
// complement: sigma(~a) = ~sigma(a).
if (rex.is_complement(r, a))
return mk_compl(mk_fromre(a));
// complement: sigma(~a). Prefer the symbolic-derivative rule to avoid the De
// Morgan 2^k blow-up: r = E(~a) | RE(LF(delta(~a))), peel one character and
// recurse. Fall back to the De Morgan rule sigma(~a)=~sigma(a) at a
// complemented star ~(R*) or on a cyclic revisit (both keep it terminating).
if (rex.is_complement(r, a)) {
expr_ref nb = m_rw.is_nullable(r); // nullable(~a)
if (!rex.is_star(a) && !rex.is_plus(a) && !deriv_memo.contains(r)
&& (m.is_true(nb) || m.is_false(nb))) {
deriv_memo.insert(r);
sort* re_sort = rex.mk_re(seq_sort);
expr_ref unfolded(m);
if (m.is_true(nb)) unfolded = rex.mk_epsilon(seq_sort); // E(~a) = eps
else unfolded = rex.mk_empty(re_sort); // E(~a) = bot
expr_ref_pair_vector cofs(m);
m_rw.brz_derivative_cofactors(r, cofs); // {(alpha_i, tgt_i)} = LF(delta(~a))
for (auto const& [cond, tgt] : cofs) {
expr_ref alpha = mk_charclass_re(cond); // single-char regex
expr_ref term(rex.mk_concat(alpha, tgt), m); // alpha_i . tgt_i
unfolded = expr_ref(rex.mk_union(unfolded, term), m);
}
return mk_fromre(unfolded);
}
return mk_compl(mk_fromre(a)); // De Morgan fallback
}
// abbreviation
// difference: a \ b = a & ~b ; sigma(a \ b) = sigma(a) cap ~sigma(b).
@ -487,7 +518,8 @@ expr_ref seq_split::from_split_set(split_set const& s) {
}
expr_ref seq_split::head_normalize(expr* t, split_mode mode, unsigned threshold,
split_oracle const& oracle, bool& ok) {
split_oracle const& oracle, bool& ok,
obj_hashtable<expr>& deriv_memo) {
ok = true;
expr *a = nullptr, *b = nullptr, *r = nullptr, *s = nullptr;
@ -498,23 +530,23 @@ expr_ref seq_split::head_normalize(expr* t, split_mode mode, unsigned threshold,
// from_re(r): one level of sigma; recurse to settle a non-frontier head
// (plus / inter / compl / diff expand to lcat / inter / compl nodes).
if (is_fromre(t, r)) {
expr_ref e = expand_fromre(r, ok);
expr_ref e = expand_fromre(r, ok, deriv_memo);
if (!ok)
return expr_ref(m);
if (is_frontier(e))
return e;
return head_normalize(e, mode, threshold, oracle, ok);
return head_normalize(e, mode, threshold, oracle, ok, deriv_memo);
}
// r.S : head-normalize S, then distribute r over the frontier.
if (is_lcat(t, r, s)) {
expr_ref hs = head_normalize(s, mode, threshold, oracle, ok);
expr_ref hs = head_normalize(s, mode, threshold, oracle, ok, deriv_memo);
if (!ok)
return expr_ref(m);
return distribute_lcat(r, hs);
}
if (is_rcat(t, s, r)) {
expr_ref hs = head_normalize(s, mode, threshold, oracle, ok);
expr_ref hs = head_normalize(s, mode, threshold, oracle, ok, deriv_memo);
if (!ok)
return expr_ref(m);
return distribute_rcat(hs, r);
@ -601,7 +633,7 @@ bool seq_split::iterator::next(expr_ref& out_d, expr_ref& out_n) {
m_work.pop_back();
bool ok = true;
expr_ref hn = m_engine.head_normalize(t, m_mode, m_threshold, m_oracle, ok);
expr_ref hn = m_engine.head_normalize(t, m_mode, m_threshold, m_oracle, ok, m_deriv_memo);
if (!ok) {
m_giveup = true; // unsupported / weak Boolean / overrun
++m_engine.m_stats.m_giveups;

13
src/ast/rewriter/seq_split.h
View file

@ -27,6 +27,7 @@ Author:
#include "ast/seq_decl_plugin.h"
#include "ast/rewriter/seq_subset.h"
#include "util/obj_hashtable.h"
#include <functional>
class seq_rewriter;
@ -134,7 +135,10 @@ class seq_split {
// One level of the sigma rules: from_re(r) -> a SplitSet term built from the
// immediate subterms. `ok` is set false on an unsupported shape.
expr_ref expand_fromre(expr* r, bool& ok);
expr_ref expand_fromre(expr* r, bool& ok, obj_hashtable<expr>& deriv_memo);
// Build the single-character regex of_pred(lambda c. pred) from a cofactor
// path condition `pred` (a Boolean over the character (:var 0)).
expr_ref mk_charclass_re(expr* pred);
// Distribute a left/right concatenation over a head-normal split-set.
expr_ref distribute_lcat(expr* r, expr* hs);
expr_ref distribute_rcat(expr* hs, expr* r);
@ -146,7 +150,8 @@ class seq_split {
// `ok` is set false on a give-up (unsupported shape, weak-mode Boolean, or
// threshold overrun).
expr_ref head_normalize(expr* t, split_mode mode, unsigned threshold,
split_oracle const& oracle, bool& ok);
split_oracle const& oracle, bool& ok,
obj_hashtable<expr>& deriv_memo);
// Fully drain a suspended split-set into `out` (used for inter/compl bodies).
// Runs an `iterator` to exhaustion; returns false on a give-up.
bool materialize(expr* node, split_mode mode, unsigned threshold,
@ -204,6 +209,10 @@ public:
expr_ref_vector m_work; // GC-safe worklist of suspended split-sets
unsigned m_count = 0; // splits produced so far (vs. threshold)
bool m_giveup = false;
// Complement ~-regex states already expanded via the symbolic-derivative
// rule; re-encountering one (a cycle) falls back to the De Morgan rule so
// the lazy unfolding terminates. Per-iterator (iterators run concurrently).
obj_hashtable<expr> m_deriv_memo;
public:
iterator(seq_split& engine, expr* node, split_mode mode,
unsigned threshold, split_oracle oracle);