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Add OP_RE_XOR and union-find bisimulation for ground regex equivalence (#9804)

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Implements the algorithm of Eq(p,q) = Empty(p XOR q)' using a union-find
driven bisimulation closure (per the CAV'26 ERE paper).

### What's added

* **New primitive OP_RE_XOR (re.xor)** wired through seq_decl_plugin:
parser signature, info propagation (nullable, min_length), and
pretty-printer.
* **seq_rewriter**: structural XOR rewrites ( XOR r = empty, XOR empty =
r, ull XOR r = comp(r), comp/comp absorption, complement push, AC
normalisation), nullability (Null(p XOR q) = Null(p) != Null(q)),
derivative (D_a(p XOR q) = D_a(p) XOR D_a(q)), reverse, antimirov
derivative, and `check_deriv_normal_form` coverage.
* **New class seq::regex_bisim** in
`src/ast/rewriter/seq_regex_bisim.{h,cpp}` to keep the bisim logic out
of the already-large `seq_rewriter.cpp`. Uses `basic_union_find` from
`util/union_find.h`, an `obj_map` for the node assignment, and a
50000-step bound (returns `l_undef` on overrun).
* **Integration** in `seq_rewriter::reduce_re_eq` (with a re-entry
guard) and in `seq_regex::propagate_eq` / `propagate_ne` for ground
regexes; on `l_undef` we fall back to the existing axiomatisation.
* **`sls_seq_plugin`**: extend `OP_RE_DIFF` switch arms to also cover
`OP_RE_XOR`.

### Validation

* Full release build with MSVC + Ninja.
* `./test-z3 /a` -- 89/89 tests passing.
* `./test-z3 /seq smt2print_parse` -- PASS.
* Smoke tests with `(a|b)*` vs `(a*b*)*` (equal) and `a*` vs `(a|b)*`
(not equal) return the expected `sat`/`unsat` quickly.

---------

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
This commit is contained in:
Margus Veanes 2026-06-10 14:58:20 -07:00 • committed by GitHub
parent 589bd9e6f5
commit 513b81253b
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GPG key ID: B5690EEEBB952194
9 changed files with 664 additions and 20 deletions
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5
src/ast/seq_decl_plugin.h
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@ -68,6 +68,7 @@ enum seq_op_kind {
OP_RE_UNION,
OP_RE_DIFF,
OP_RE_INTERSECT,
OP_RE_XOR,
OP_RE_LOOP,
OP_RE_POWER,
OP_RE_COMPLEMENT,
@ -491,6 +492,7 @@ public:
info disj(info const& rhs) const;
info conj(info const& rhs) const;
info diff(info const& rhs) const;
info xor_(info const& rhs) const;
info orelse(info const& rhs) const;
info loop(unsigned lower, unsigned upper) const;
@ -523,6 +525,7 @@ public:
app* mk_union(expr* r1, expr* r2) { return m.mk_app(m_fid, OP_RE_UNION, r1, r2); }
app* mk_inter(expr* r1, expr* r2) { return m.mk_app(m_fid, OP_RE_INTERSECT, r1, r2); }
app* mk_diff(expr* r1, expr* r2) { return m.mk_app(m_fid, OP_RE_DIFF, r1, r2); }
app* mk_xor(expr* r1, expr* r2) { return m.mk_app(m_fid, OP_RE_XOR, r1, r2); }
app* mk_complement(expr* r) { return m.mk_app(m_fid, OP_RE_COMPLEMENT, r); }
app* mk_star(expr* r) { return m.mk_app(m_fid, OP_RE_STAR, r); }
app* mk_plus(expr* r) { return m.mk_app(m_fid, OP_RE_PLUS, r); }
@ -546,6 +549,7 @@ public:
bool is_union(expr const* n) const { return is_app_of(n, m_fid, OP_RE_UNION); }
bool is_intersection(expr const* n) const { return is_app_of(n, m_fid, OP_RE_INTERSECT); }
bool is_diff(expr const* n) const { return is_app_of(n, m_fid, OP_RE_DIFF); }
bool is_xor(expr const* n) const { return is_app_of(n, m_fid, OP_RE_XOR); }
bool is_complement(expr const* n) const { return is_app_of(n, m_fid, OP_RE_COMPLEMENT); }
bool is_star(expr const* n) const { return is_app_of(n, m_fid, OP_RE_STAR); }
bool is_plus(expr const* n) const { return is_app_of(n, m_fid, OP_RE_PLUS); }
@ -578,6 +582,7 @@ public:
MATCH_BINARY(is_union);
MATCH_BINARY(is_intersection);
MATCH_BINARY(is_diff);
MATCH_BINARY(is_xor);
MATCH_BINARY(is_range);
MATCH_UNARY(is_complement);
MATCH_UNARY(is_star);