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We present a novel length-aware solving algorithm for the quantifier-free first-order theory over regex membership predicate and linear arithmetic over string length. We implement and evaluate this algorithm and related heuristics in the Z3 theorem prover. A crucial insight that underpins our algorithm is that real-world regex and string formulas contain a wealth of information about upper and lower bounds on lengths of strings, and such information can be used very effectively to simplify operations on automata representing regular expressions. Additionally, we present a number of novel general heuristics, such as the prefix/suffix method, that can be used to make a variety of regex solving algorithms more efficient in practice. We showcase the power of our algorithm and heuristics via an extensive empirical evaluation over a large and diverse benchmark of 57256 regex-heavy instances, almost 75% of which are derived from industrial applications or contributed by other solver developers. Our solver outperforms five other state-of-the-art string solvers, namely, CVC4, OSTRICH, Z3seq, Z3str3, and Z3-Trau, over this benchmark, in particular achieving a speedup of 2.4$$\times $$ × over CVC4, 4.4$$\times $$ × over Z3seq, 6.4$$\times $$ × over Z3-Trau, 9.1$$\times $$ × over Z3str3, and 13$$\times $$ × over OSTRICH.

We present Woorpje, a string solver for bounded word equations (i.e., equations where the length of each variable is upper bounded by a given integer). Our algorithm works by reformulating the satisfiability of bounded word equations as a reachability problem for nondeterministic finite automata, and then carefully encoding this as a propositional satisfiability problem, which we then solve using the well-known Glucose SAT-solver. This approach has the advantage of allowing for the natural inclusion of additional linear length constraints. Our solver obtains reliable and competitive results and, remarkably, discovered several cases where state-of-the-art solvers exhibit a faulty behaviour.

On the dual post correspondence problem his item ws sumitted to voughorough niversity9s snstitutionl epository y theGn uthorF Citation: heD tFhFD ishixfegrD hF nd grxishiD tFgFD PHIQF yn the dul post orrespondene prolemF sxX f¡ elD wFF nd grtonD yF @edsAF hevelopments in vnguge heoryX IUth snterntionl gonfereneD hv PHIQD wrneElEll¡ eeD prneD tune IVEPID PHIQD roeedingsF veture xotes in gomE puter iene @inluding suseries veture xotes in ertifiil sntelligene nd veture xotes in fioinformtisAY UWHUD ppFITUEIUVF Abstract. The Dual Post Correspondence Problem asks whether, for a given word α, there exists a pair of distinct morphisms σ, τ , one of which needs to be non-periodic, such that σ(α) = τ (α) is satisfied. This problem is important for the research on equality sets, which are a vital concept in the theory of computation, as it helps to identify words that are in trivial equality sets only.Little is known about the Dual PCP for words α over larger than binary alphabets. In the present paper, we address this question in a way that simplifies the usual method, which means that we can reduce the intricacy of the word equations involved in dealing with the Dual PCP. Our approach yields large sets of words for which there exists a solution to the Dual PCP as well as examples of words over arbitrary alphabets for which such a solution does not exist.

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