The Power of Commuting with Finite Sets of Words

Kunc, Michal

doi:10.1007/s00224-006-1321-z

Cited by 40 publications

(21 citation statements)

References 17 publications

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“…Some of the problems discussed in this work are similar to those in the recent decision procedure literature, but focuses more on complexity bounds and decidability results. Kunc provides an overview of this area [14,13]. The idea of treating a constraint solving problem as an explicit search problem is not new; many existing decision procedures are built around backtracking search (e.g., [24]).…”

Section: Related Workmentioning

confidence: 99%

Solving string constraints lazily

Hooimeijer

Weimer

2010

Proceedings of the IEEE/ACM International Conference on Automated Software Engineering

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Decision procedures have long been a fixture in program analysis, and reasoning about string constraints is a key element in many program analyses and testing frameworks. Recent work on string analysis has focused on providing decision procedures that model string operations. Separating string analysis from its client applications has important and familiar benefits: it enables the independent improvement of string analysis tools and it saves client effort.We present a constraint solving algorithm for equations over string variables. We focus on scalability with regard to the size of the input constraints. Our algorithm performs an explicit search for a satisfying assignment; the search space is constructed lazily based on an automata representation of the constraints. We evaluate our approach by comparing its performance with that of existing string decision procedures. Our prototype is, on average, several orders of magnitude faster than the fastest existing implementation.

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Section: Related Workmentioning

confidence: 99%

Solving string constraints lazily

Hooimeijer

Weimer

2010

Proceedings of the IEEE/ACM International Conference on Automated Software Engineering

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“…This could be implemented using basic operations on nondeterministic finite state automata that are similar to the ones already implemented. Many other features, however, would make the RMA problem undecidable in general (e.g., [27]). We instead focus on a decidable theory with a provably correct core algorithm, and leave additional features for future work.…”

Section: Extensionsmentioning

confidence: 99%

A decision procedure for subset constraints over regular languages

HooimeijerPieter

WeimerWestley

2009

SIGPLAN Not.

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Reasoning about string variables, in particular program inputs, is an important aspect of many program analyses and testing frameworks. Program inputs invariably arrive as strings, and are often manipulated using high-level string operations such as equality checks, regular expression matching, and string concatenation. It is difficult to reason about these operations because they are not well-integrated into current constraint solvers.We present a decision procedure that solves systems of equations over regular language variables. Given such a system of constraints, our algorithm finds satisfying assignments for the variables in the system. We define this problem formally and render a mechanized correctness proof of the core of the algorithm. We evaluate its scalability and practical utility by applying it to the problem of automatically finding inputs that cause SQL injection vulnerabilities.

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“…A partial explanation to the lack of such results was revealed recently when it was shown in a number of papers, how powerful or difficult language equations are. To mention a few examples, it is shown in [12] that even the question whether or not, for given finite sets A, B, C, D, E, F , the equation AB i C = DE i F holds for all i ≥ 0, is recursively undecidable, see also [14]; the maximal set commuting with a given finite set A need not be recursive, see [13]; or the fact that two given finite sets A and B are conjugate, i.e., that there exists a set Z such that AZ = ZB holds, is known to be decidable only in the case of bifix sets, see [4].…”

Section: Introductionmentioning

confidence: 99%

Unique Decipherability in the Monoid of Languages: An Application of Rational Relations

Choffrut

Karhumäki

2011

Theory Comput Syst

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Abstract. We attack the problem of deciding whether a finite collection of finite languages is a code, that is, possesses the unique decipherability property in the monoid of finite languages. We investigate a few subcases where the theory of rational relations can be employed to solve the problem. The case of unary languages is one of them and as a consequence, we show how to decide for two given finite subsets of nonnegative integers, whether they are the n-th root of a common set, for some n ≥ 1. We also show that it is decidable whether a finite collection of finite languages is a Parikh code, in the sense that whenever two products of these sets are commutatively equivalent, so are the sequences defining these products. Finally, we consider a nonunary special case where all finite sets consist of words containing exactly one occurrence of the specific letter.

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The Power of Commuting with Finite Sets of Words

Cited by 40 publications

References 17 publications

Solving string constraints lazily

Solving string constraints lazily

A decision procedure for subset constraints over regular languages

Unique Decipherability in the Monoid of Languages: An Application of Rational Relations

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