mirror of
https://github.com/Z3Prover/z3
synced 2026-06-20 07:36:31 +00:00
113 lines
4.6 KiB
C++
113 lines
4.6 KiB
C++
/*++
|
|
Copyright (c) 2026 Microsoft Corporation
|
|
|
|
Module Name:
|
|
|
|
seq_split.h
|
|
|
|
Abstract:
|
|
|
|
Regex split decomposition: the split function sigma from the paper
|
|
"Solving by Splitting". For a regular expression r, sigma(r) is a finite
|
|
"split-set" of pairs { <D_i, N_i> } such that
|
|
|
|
u.v in L(r) iff exists i: u in L(D_i) and v in L(N_i).
|
|
|
|
This lifts the decomposition previously buried in the nseq solver
|
|
(seq::compute_sigma over euf::snode) into a self-contained, expr*-based
|
|
engine that can be reused anywhere a seq_rewriter is available (the legacy
|
|
seq solver, nseq, and the regex rewriter itself).
|
|
|
|
The split algebra (intersection, De Morgan complement, left/right
|
|
concatenation with a regex) and the cardinality-reducing simplification
|
|
heuristics (drop bottom, same-D/same-N merge, subsumption via seq_subset)
|
|
follow the paper.
|
|
|
|
Author:
|
|
|
|
Nikolaj Bjorner (nbjorner) 2026-6-10
|
|
Clemens Eisenhofer 2026-6-10
|
|
|
|
--*/
|
|
#pragma once
|
|
|
|
#include "ast/seq_decl_plugin.h"
|
|
#include "ast/rewriter/seq_subset.h"
|
|
#include <functional>
|
|
|
|
class seq_rewriter;
|
|
|
|
// An individual split <D, N>: the left (prefix) regex D and right (suffix)
|
|
// regex N. u.v in L(r) for this split iff u in L(D) and v in L(N).
|
|
struct split_pair {
|
|
expr_ref m_d;
|
|
expr_ref m_n;
|
|
split_pair(expr* d, expr* n, ast_manager& m) : m_d(d, m), m_n(n, m) {
|
|
SASSERT(d && n);
|
|
}
|
|
};
|
|
|
|
// A split-set is a union of individual splits.
|
|
typedef vector<split_pair> split_set;
|
|
|
|
// Controls how aggressively sigma expands the Boolean-closure cases:
|
|
// strong - fully expand complement / intersection via the split algebra
|
|
// (De Morgan / cross product). This is the behaviour the nseq
|
|
// solver relies on.
|
|
// weak - do not perform the (potentially 2^k) Boolean-closure expansion;
|
|
// give up (return false) on complement / intersection instead.
|
|
enum class split_mode { weak, strong };
|
|
|
|
// Optional lookahead oracle. Called for each candidate split <D, N> as it is
|
|
// generated; returns true to keep it, false to prune it. An empty oracle (the
|
|
// default) keeps everything, so sigma is unchanged. See seq_split::compute.
|
|
typedef std::function<bool(expr* D, expr* N)> split_oracle;
|
|
|
|
class seq_split {
|
|
seq_rewriter& m_rw; // for mk_re_append + manager / seq_util access
|
|
seq_subset m_subset; // language-subset checks for subsumption
|
|
|
|
ast_manager& m() const;
|
|
seq_util& seq() const;
|
|
seq_util::rex& re() const;
|
|
|
|
// Push <d, n> onto `out`, unless `oracle` rejects it.
|
|
void push(split_set& out, split_oracle const& oracle, expr* d, expr* n) const;
|
|
|
|
// S1 cap S2 = { <D1 cap D2, N1 cap N2> } dropping any pair with a bottom
|
|
// component (and any rejected by `oracle`). Returns false on threshold overrun.
|
|
bool intersect(split_set const& s1, split_set const& s2, split_set& result,
|
|
unsigned threshold, split_oracle const& oracle);
|
|
|
|
// De Morgan complement of a split-set: ~S = cap_{s in S} ~s with
|
|
// ~<D,N> = { <~D, .*>, <.*, ~N> } and ~{} = { <.*, .*> }.
|
|
bool complement(sort* seq_sort, split_set const& sp, split_set& result,
|
|
unsigned threshold, split_oracle const& oracle);
|
|
|
|
// same-D / same-N merge: groups pairs that share a (syntactically identical)
|
|
// left (resp. right) component and unions the other component.
|
|
void merge_by(split_set& pairs, bool by_left) const;
|
|
|
|
public:
|
|
explicit seq_split(seq_rewriter& rw);
|
|
|
|
// Compute sigma(r), appending to `out` (does not clear it). `threshold`
|
|
// bounds the number of produced splits; an overrun, an unsupported regex
|
|
// shape (bounded loop / ite), or a Boolean-closure case in weak mode makes
|
|
// it return false ("give up").
|
|
//
|
|
// `oracle` (optional) prunes non-viable splits *during* generation. It must
|
|
// be sound to apply at every generation step: a candidate N can still gain a
|
|
// prefix from a factor appended to its right later (concat/star), so the
|
|
// oracle must use a "prefix-compatible" test (prune only when N can never
|
|
// match the lookahead, even partially), NOT a strict "starts-with" test.
|
|
// The complement body is computed WITHOUT the oracle (inverted orientation);
|
|
// the oracle is re-applied to the complement's output fold.
|
|
bool compute(expr* r, split_set& out, unsigned threshold,
|
|
split_mode mode = split_mode::strong, split_oracle const& oracle = {});
|
|
|
|
// In-place simplification of a split-set: drop bottom components, apply the
|
|
// same-D / same-N merge rules, and drop splits subsumed by another (using
|
|
// seq_subset). Size-capped to keep the O(n^2) subsumption affordable.
|
|
void simplify(split_set& s);
|
|
};
|