A Survey on String Constraint Solving

AmadiniRoberto,

doi:10.1145/3484198

Cited by 24 publications

(13 citation statements)

References 156 publications

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“…Condition (1) of Lemma 5.3 is satisfied because the relations R h 1 , R h 2 , and R h 1 ,h 2 are PE-definable in pG diag,S 1 ,S 2 , abq by Lemma 6.13 (3). We next establish that condition (2) of Lemma 5.3 is satisfied.…”

Section: Main Results For Partially Commutative Groups (Or Raags)mentioning

confidence: 81%

“…The term 'word equations' refers to equations in free monoids, and deciding algorithmically whether a word equation has solutions satisfying certain linear length constraints is a major open question: it has deep implications, both theoretical (if undecidable, it would offer a new solution to Hilbert's 10th problem about the satisfiability of polynomial equations with integer coefficients) and practical, in the context of string solvers for security analysis. We refer the reader to the surveys [3,14] for an overview of the area from several viewpoints, of both theoretical and applied nature.…”

Section: Introductionmentioning

confidence: 99%

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Group equations with abelian predicates

Ciobanu¹,

Garreta²

2022

Preprint

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In this paper we begin the systematic study of group equations with abelian predicates in the main classes of groups where solving equations is possible. We extend the line of work on word equations with length constraints, and more generally, on extensions of the existential theory of semigroups, to the world of groups.We use interpretability by equations to establish model-theoretic and algebraic conditions which are sufficient to get undecidability. We apply our results to (nonabelian) right-angled Artin groups, and show that the problem of solving equations with abelian predicates is undecidable for these. We obtain the same result for hyperbolic groups whose abelianisation has torsion-free rank at least two. By contrast, we prove that in groups with finite abelianisation, the problem can be reduced to solving equations with recognisable constraints, and so this is decidable in rightangled Coxeter groups, or more generally, graph products of finite groups, as well as hyperbolic groups with finite abelianisation.

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Section: Main Results For Partially Commutative Groups (Or Raags)mentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Group equations with abelian predicates

Ciobanu¹,

Garreta²

2022

Preprint

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“…In this section, we introduce a variety of logical theories encompassing the most common kinds of string constraints (as overviewed in [6]). We define three sets of terms as follows.…”

Section: Logical Theories Over Strings Constraintsmentioning

confidence: 99%

“…Together, the 4 types of atoms we allow cover many of the most prominent types of string constraints, as listed in [6]. While predicates related to equality between strings, concatenations of strings, and linear arithmetic over string-lengths do not need more explanations, a discussion is in order w.r.t.…”

Section: Introductionmentioning

confidence: 99%

Formal Languages via Theories over Strings

Day¹,

Grewal²,

Manea³

2022

Preprint

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We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly pushdown, and deterministic context-free languages. In total, we consider 20 distinct theories and decidability questions for problems such as emptiness and universality for formal languages over them. First, we discuss their relative expressive power and observe a rough division into two hierarchies based on whether or not word equations are present. Second, we consider the decidability status of several important decision problems, such as emptiness and universality. Note that the emptiness problem is equivalent to the satisfiability problem over the corresponding theory. Third, we consider the problem of whether a language in one theory is expressible in another and show several negative results in which this problem is undecidable. These results are particularly relevant in the context of normal forms in both practical and theoretical aspects of string solving.

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“…Recent motivations for theoretical and practical investigations in this area come from the verification of security protocols (e.g., detecting security flaws exploited in injection attacks or cross site scripting attacks) or the symbolic execution of string-heavy languages. Excellent overviews of the main definitions and fundamental results as well as of the many recent developments related to the theory and practice of string solving are [2,18].…”

Section: Introductionmentioning

confidence: 99%

A Generic Information Extraction System for String Constraints

Day¹,

Kröger²,

Kulczynski³

et al. 2022

Preprint

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String constraint solving, and the underlying theory of word equations, are highly interesting research topics both for practitioners and theoreticians working in the wide area of satisfiability modulo theories. As string constraint solving algorithms, a.k.a. string solvers, gained a more prominent role in the formal analysis of string-heavy programs, especially in connection to symbolic code execution and security protocol verification, we can witness an ever-growing number of benchmarks collecting string solving instances from real-world applications as well as an ever-growing need for more efficient and reliable solvers, especially for the aforementioned real-world instances. Thus, it seems that the string solving area (and the developers, theoreticians, and end-users active in it) could greatly benefit from a better understanding and processing of the existing string solving benchmarks. In this context, we propose SMTQuery: an SMT-LIB benchmark analysis tool for string constraints. SMTQuery is implemented in Python 3, and offers a collection of analysis and information extraction tools for a comprehensive data base of string benchmarks (presented in SMT-LIB format), based on an SQL-centred language called qlang.

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A Survey on String Constraint Solving

Cited by 24 publications

References 156 publications

Group equations with abelian predicates

Group equations with abelian predicates

Formal Languages via Theories over Strings

A Generic Information Extraction System for String Constraints

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