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seq_monadic: add light Antimirov cofactor mode (#10323)

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Light-weight Antimirov cofactors for seq_monadic
================================================

Overview
--------

The seq_monadic solver explores symbolic regex derivatives when
computing live
states and product transitions. Its original transition representation
used
Brzozowski cofactors.

This change adds a light-weight Antimirov representation. It first
computes the
existing Brzozowski cofactors and then decomposes targets whose outer
shape is

    s1 | ... | sn

or

    (s1 | ... | sn) . tail

into separate transitions. Concatenations are maintained in
right-associative
form, so a distributable union occurs as the head of the concatenation.
Targets are reconstructed with mk_regex_concat to preserve
normalization.

After decomposition, transitions with the same target are merged by
disjoining
their guards. The existing path-aware cofactor traversal and range
predicates
are therefore retained.

Example
-------

For

    r = .* a .{k}

the Brzozowski cofactors have the shape

    [a,  r | .{k}]
    [^a, r]

The light-weight Antimirov transformation produces

    [., r]
    [a, .{k}]

This preserves the language while avoiding the deterministic subset
states
that grow exponentially on this family.

Modes
-----

seq_monadic exposes two transition modes:

    light_antimirov   default
    brzozowski        retained as an explicit option

The implementation is seq_rewriter::light_ant_derivative_cofactors.

Correctness
-----------

The seq_monadic unit tests run in both modes. They cover character and
generic
element sequences, multiple and repeated variables, variable
constraints,
bounded loops, conjunctions of memberships, and witness construction. A
focused test checks the cofactor transformation above. The complete
94-test
unit suite used during evaluation passed. The benchmark harness is not
registered as a normal unit test; after detaching it, all 93 registered
tests
pass.

Benchmark evaluation
--------------------

The final optimized comparison used all 1,545 SMT2 files under
C:\git\bench\inputs\regexes. Each file was run in a separate process
with a
15-second timeout. There were 1,513 cases where both modes completed
without a
process failure or timeout.

                                    Brzozowski       Light-Ant
    paired solver time                 94.98 s          63.26 s
    median solver time                  1.734 ms         0.710 ms
    derivative calls                    5.70 M           3.39 M
    cofactors                           13.33 M           6.99 M
    live states                          2.74 M           0.44 M
    product states                     652.8 K         642.8 K

Light-Ant reduced paired solver time by 33.4%, derivative calls by
40.5%,
cofactors by 47.5%, and live states by 84.0%. It was faster on 1,091
cases;
Brzozowski was faster on 421 cases.

Light-Ant changed 131 Brzozowski undef results to sat. There were no
reverse
verdict changes and no mismatches against known sat/unsat statuses. Both
modes
had two timeouts. Process failures decreased from 30 to 27.

By corpus, paired solver time improved by 39.1% on ClemensRegex and by
11.9% on
MargusRegex.

Alternatives considered
-----------------------

Direct use of full Antimirov derivatives was also evaluated. It
introduced
large performance outliers, particularly around intersections, and
produced
additional undef results and timeouts. Disabling intersection-over-union
distribution improved some of these cases but remained slower and less
robust
than the light-weight transformation. The direct full-Ant mode was
therefore
removed from this change.

Copilot-Session: a2ce3573-4e15-4a4a-afb5-21e3cb04e4a2
This commit is contained in:
Margus Veanes 2026-07-31 10:34:34 -07:00 • committed by GitHub
parent 214726519d
commit 683cb4ec03
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GPG key ID: B5690EEEBB952194
5 changed files with 152 additions and 11 deletions
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22
src/ast/rewriter/seq_monadic.h
View file

@ -15,9 +15,9 @@ Abstract:
derivatives).
Self-contained decision procedure: NO Nielsen splitting (seq_split), NO minterms,
and NO materialization of reach(q) as a regex. It relies only on the symbolic
Brzozowski derivative (brz_derivative_cofactors as a transition regex) and on
automaton product-reachability for emptiness.
and NO materialization of reach(q) as a regex. It uses symbolic derivative
cofactors as Brzozowski states or Brzozowski states post-processed into
light-weight Antimirov states, and automaton product-reachability for emptiness.
Method. For a term x.u in R and the whole-language split, x drives the derivative
automaton of R from R to some live state q, and the rest u must be accepted from q:
@ -59,10 +59,18 @@ Author:
#include <utility>
class seq_monadic {
public:
enum class transition_mode {
brzozowski,
light_antimirov
};
private:
ast_manager& m;
seq_rewriter& m_rw;
th_rewriter m_thrw; // normalizes constant-element derivatives (folds
// ground guards so dead states become re.empty)
transition_mode m_mode;
sort* m_seq_sort = nullptr; // sequence sort of the regex under analysis
sort* m_elem_sort = nullptr; // element sort of that sequence sort
expr_ref_vector m_pin; // pins derivative states / witnesses referenced later
@ -86,6 +94,9 @@ class seq_monadic {
// Brzozowski derivative of regex `r` by the concrete element `elem`.
expr_ref der_elem(expr* r, expr* elem);
// Symbolic transition cofactors in the selected mode.
void derivative_cofactors(expr* r, expr_ref_pair_vector& result);
// Live reachable derivative states of R (BFS over cofactor targets + liveness
// least-fixpoint). These are the split states q. Sets `ok` false on a cap overrun.
void live_states(expr* R, ptr_vector<expr>& out, bool& ok);
@ -119,7 +130,10 @@ class seq_monadic {
obj_map<expr, expr*>* model);
public:
seq_monadic(seq_rewriter& rw) : m(rw.m()), m_rw(rw), m_thrw(rw.m()), m_pin(rw.m()) {}
seq_monadic(seq_rewriter& rw, transition_mode mode = transition_mode::light_antimirov) :
m(rw.m()), m_rw(rw), m_thrw(rw.m()), m_mode(mode), m_pin(rw.m()) {}
transition_mode mode() const { return m_mode; }
// Decide (str.in_re term R) for a term that is a concatenation of string variables
// (possibly repeated / several distinct) and constant characters.