On Solving Word Equations Using SAT

Day, Joel D.; Ehlers, Thorsten; Kulczynski, Mitja; Manea, Florín; Nowotka, Dirk; Poulsen, Danny Bøgsted

doi:10.1007/978-3-030-30806-3_8

Cited by 20 publications

(15 citation statements)

References 17 publications

(30 reference statements)

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“…Finally, we have aimed to test the scheme Spec(µ(WICount), Go(v , Φ 1 = Φ 2 )) in a more practical case, if Φ 1 = Φ 2 is chosen at random. For this purpose we use a set of equations provided in the paper [5] as a benchmark for the string constraint solver Woorpje, namely Track 1 consisting of 200 random equations. We have removed the length constraints from the benchmark before the specialization.…”

Section: Specialization Of Interpreter Wicountmentioning

confidence: 99%

“…In recent decades, program transformation techniques were applied in verification of properties of several models, including cache-coherence and cryptographic protocols, and Petri nets. On the other hand, the number of works on verification for string manipulating programs and string constraint solvers is growing rapidly last years [1,2,5,12,13,14,24,28,31].…”

Section: Introductionmentioning

confidence: 99%

“…These sets are not covered in the recent works on the string constraint solvers in the unbounded case. Finally, we discuss the results of the verification for the set of arbitrary equations generated as a benchmark for the solver Woorpje [5], but in the case the solution lengths are unbounded. Surprisingly, complete solution graphs are generated for the most of these equations, although they do not belong to any special set for which the specialization is guaranteed to succeed.…”

Section: Introductionmentioning

confidence: 99%

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Program Specialization as a Tool for Solving Word Equations

Nepeivoda¹

2021

Electron. Proc. Theor. Comput. Sci.

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The paper focuses on the automatic generating of the witnesses for the word equation satisfiability problem by means of specializing an interpreter WI L ( σ i , Eqs), which tests whether a composition of variable substitutions σ i of a given word equation system Eqs produces its solution. We specialize such an interpreter w.r.t. Eqs, while σ i are unknown. We show that several variants of such interpreters, when specialized using the basic unfold/fold methods, are able to construct the whole solution sets for some classes of the word equations whose left-and right-hand sides share variables. We prove that the specialization process w.r.t. the constructed interpreters gives a simple syntactic criterion of the satisfiability of the equations considered, and show that the suggested approach can solve some equations not solvable by Z3str3 and CVC4, the widely-used SMT-solvers.* The reported study was partially supported by Russian Academy of Sciences, research project No. AAAA-A19-119020690043-9. 1 We use the assumption that only the elements c belonging to the function domain are considered, which is expressed by the premise ∃ f (c).AddExprMS((Vs sym )++x expr , xms) = AddExprMS(x expr , Include((Vs sym ), ε, xms)); AddExprMS(s sym ++x expr , xms) = AddExprMS(x expr , Include(s sym , ε, xms)); AddExprMS(ε, (xms)) = xms;

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Section: Specialization Of Interpreter Wicountmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Program Specialization as a Tool for Solving Word Equations

Nepeivoda¹

2021

Electron. Proc. Theor. Comput. Sci.

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“…Indeed, this model arises naturally in, e.g., tasks related to formal analysis of string-heavy programs such as sanitization and validation of inputs (cf. [28]), leading to the development of multiple string solvers such as CVC4 [7], Z3seq [10], Z3str3 [8], and Woorpje [14]. Even though these solvers are quite efficient for certain practical use cases, novel applications demand even more efficient and reliable techniques, especially for real-world inputs.…”

Section: Introductionmentioning

confidence: 99%

String Theories involving Regular Membership Predicates: From Practice to Theory and Back

Berzish¹,

Day²,

Kulczynski³

et al. 2021

Preprint

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Widespread use of string solvers in formal analysis of stringheavy programs has led to a growing demand for more efficient and reliable techniques which can be applied in this context, especially for real-world cases. Designing an algorithm for the (generally undecidable) satisfiability problem for systems of string constraints requires a thorough understanding of the structure of constraints present in the targeted cases. In this paper, we investigate benchmarks presented in the literature containing regular expression membership predicates, extract different first order logic theories, and prove their decidability, resp. undecidability. Notably, the most common theories in real-world benchmarks are PSPACE-complete and directly lead to the implementation of a more efficient algorithm to solving string constraints.

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“…This chapter is based on work being published at RP 2019 [40], For-maliSE 2020 [42], CAV 2021 [24], and WORDS 2021 [22].…”

Section: Different Techniques To Solvingmentioning

confidence: 99%

Light On String Solving

Kulczynski¹

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Widespread use of string solvers in formal analysis of string-heavy programs has led to a growing demand for more efficient and reliable techniques which can be applied in this context, especially for real-world cases. Designing an algorithm for the (generally undecidable) satisfiability problem for systems of string constraints requires a thorough understanding of the structure of constraints present in the targeted cases. We target the aforementioned case in different perspectives: We present an algorithm which works by reformulating the satisfiability of bounded word equations as a reachability problem for non-deterministic finite automata. Secondly, we present a transformation-system-based technique to solving string constraints. Thirdly, we investigate benchmarks presented in the literature containing regular expression membership predicates and design a decission procedure for a PSPACE-complete sub-theory. Additionally, we introduce a new benchmarking framework for string solvers and use it to showcase the power of our algorithms via an extensive empirical evaluation over a diverse set of benchmarks.

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On Solving Word Equations Using SAT

Cited by 20 publications

References 17 publications

Program Specialization as a Tool for Solving Word Equations

Program Specialization as a Tool for Solving Word Equations

String Theories involving Regular Membership Predicates: From Practice to Theory and Back

Light On String Solving

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