Add a standalone, minterm-free decision procedure for the regex-membership
fragment where the term is a concatenation of string variables and constant
characters (e.g. x.a.x in R), based on a whole-language split + monadic
decomposition. It does NOT use Nielsen word-equation splitting and does NOT
touch seq_split.
x.u in r <=> OR_i ( x in reach(q_i) /\ u in q_i ) over sigma(r)
reach(q) is never materialized as a regex (regex/GNFA state-elimination blows
up super-polynomially, k! on lattice-shaped automata). Instead a variable's
constraint is a conjunction of components <state0,target> and emptiness is
decided by a lazy automaton PRODUCT-REACHABILITY BFS over tuples of component
states: transitions are the cartesian product of brz_derivative_cofactors
branches with pairwise-conjoined seq::range_predicate guards (the fast,
canonical range algebra) - minterm-free throughout. A global work budget bails
to l_undef on the rare many-occurrence blowup. Termination is by finiteness of
ACI-canonical derivative states.
Wire it as a log-only diagnostic in theory_nseq::final_check_eh behind
IF_VERBOSE(1): group compound memberships per term (intersecting regexes),
build per-variable base constraints, and log MONADIC-VERDICT ... time-ms. The
change is purely additive and inert at -v:0; production solving is unchanged.
Add tst_seq_monadic (23 cases): nested complement (L3-02 unsat, L3-03 sat),
multiple/repeated variables (x.a.y, x.y.x), per-variable base constraints, and
the bounded-loop regression x.y.x in [0-9]{n} (exercises live_states on a
counted automaton).
Over the 325 multivariable-membership benchmarks the diagnostic decides 249,
of which 230 agree with the authoritative status; the only 2 mismatches are a
length-only limitation (|x|=2k not yet extracted) in the safe direction
(sat-where-unsat-by-length). 0 unsound unsat, 0 crashes. Up to ~23,500x faster
than the Nielsen path on the nested-complement / counted-complement class.
Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
