Multiple regex membership heuristic

[jurajsic]

This PR adds heuristic for formulae where we only have regex membership predicates (or formulae that are easily tranformed to this form). For each var x, it takes all x in RE or x not in RE and sorts the regexes by the sum of loops occurring in the regexes, with the regexes that need to be complemented being at the end. Then it lazily computes the intersection of all these regexes, so that if we get an empty language, we can immediately say UNSAT without continuing building the more complex regexes.

[jurajsic]

On automatark:

Benchmark automatark
# of formulae: 15995
--------------------------------------------------
tool                                                ✅    ❌      time    avg    med    std    sat    unsat    unknown    TO    MO+ERR    other
-----------------------------------------------  -----  ----  --------  -----  -----  -----  -----  -------  ---------  ----  --------  -------
z3-noodler-da892c5-d95fe13                       15979    16    553.24   0.03   0.01   0.37  10466     5513          0    16         0        0
z3-noodler-e58cb97-d95fe13                       15970    25    904.53   0.06   0.01   0.67  10466     5504          0    25         0        0
cvc5-1.1.2                                       15902    93   2216.97   0.14   0.00   2.83  10460     5442          0    85         8        0
z3-4.13.0                                        15870   125   6425.06   0.40   0.02   3.90  10469     5401          0   124         1        0
ostrich-5dd2e10ca                                15947    48  24332.97   1.53   1.41   1.89  10440     5507          0    48         0        0
z3-noodler-914a49e-d95fe13                       15973    22    790.39   0.05   0.01   0.51  10466     5507          0    22         0        0
z3-4.13.0+cvc5-1.1.2                             15969    26    543.82   0.03   0.00   1.22  10481     5488         26     0         0        0
z3-noodler-da892c5-d95fe13+cvc5-1.1.2            15992     3    116.10   0.01   0.00   0.16  10478     5514          3     0         0        0
z3-noodler-da892c5-d95fe13+z3-4.13.0             15995     0    296.15   0.02   0.01   0.16  10481     5514          0     0         0        0
z3-noodler-da892c5-d95fe13+z3-4.13.0+cvc5-1.1.2  15995     0     76.14   0.00   0.00   0.04  10481     5514          0     0         0        0
--------------------------------------------------

We can handle all (except one) UNSAT cases, there are still 15 SAT cases for which this heuristic will not help.

[jurajsic]

Final results:

# of formulae: 103318
--------------------------------------------------
tool                                                 ✅     ❌       time    avg    med    std    sat    unsat    unknown     TO    MO+ERR    other
-----------------------------------------------  ------  -----  ---------  -----  -----  -----  -----  -------  ---------  -----  --------  -------
z3-noodler-7380a2a-d95fe13                       102134   1184   12821.32   0.13   0.01   1.63  62771    39363        636    495        53        0
z3-noodler-e58cb97-d95fe13                       102120   1198   13149.57   0.13   0.01   1.55  62768    39352        636    509        53        0
cvc5-1.1.2                                        99699   3619   76478.24   0.77   0.00   6.77  60798    38901          2   3608         9        0
z3-4.13.0                                         97687   5631  132036.99   1.35   0.01   8.11  58874    38813        210   4960       461        0
ostrich-5dd2e10ca                                 86344  16974  782639.00   9.06   1.75  19.20  47556    38788          0  16962         0       12
z3-4.13.0+cvc5-1.1.2                             100756   2562   60604.78   0.60   0.00   6.00  61099    39657       2562      0         0        0
z3-noodler-7380a2a-d95fe13+cvc5-1.1.2            103177    141    9307.48   0.09   0.00   1.42  63261    39916        141      0         0        0
z3-noodler-7380a2a-d95fe13+z3-4.13.0             102785    533    9756.39   0.09   0.01   1.04  62956    39829        533      0         0        0
z3-noodler-7380a2a-d95fe13+z3-4.13.0+cvc5-1.1.2  103190    128    8811.23   0.09   0.00   1.45  63270    39920        128      0         0        0
--------------------------------------------------

No impact on other benchmarks, as expected.