Path Feasibility Analysis for String-Manipulating Programs

Bjørner, Nikolaj; Tillmann, Nikolai; Воронков, Андрей

doi:10.1007/978-3-642-00768-2_27

Cited by 142 publications

(170 citation statements)

References 20 publications

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“…. , p n )) such that for each i and each (1 ≤ j ≤ n), θ i (p j ) = t j and if the values' set is not empty we choose: (1) in the case of the language L, the only Markov substitution; (2) in the case of the language L * , nondeterministically one from the substitutions. In the second case the variables should be subscripted by the required indices.…”

Section: On Semantics Of the Pattern Matchingmentioning

confidence: 99%

“…Since ln(g) < ln(t), the variant (3.b) can be involved by the case (3) at most finitely many times. (3.c) If t= #e.w ++ g, then let π be the following Markov relation (#e.w = #e.w c [1] ++ c ++ #e.r c [1] ), where #e.w c [1] , #e.r c [1] are fresh parameters.…”

Section: Inductive Stepmentioning

confidence: 99%

“…By the inductive assumption, we can compute the set R 1 = → Π, Θ (q ++ e.z, #e.r c [1] ++ gπ), but the pure concatenation of two narrowings π and π 1 from R 1 may lead to an incorrect narrowing π; π 1 since, by Markov's rule, the unknown string #e.w c [1] does not contain the character c and this restriction may contradict to π 1 and the semantics of p (see Section 4.1 grams written in the nondeterministic language M * results in a finite description of the solution set of the equation.…”

Section: Inductive Stepmentioning

confidence: 99%

“…Given a current state st of Int, the current call Step(st) results in the next state following immediately after st. In general, the actual execution time taken by the step evaluation is not uniformly bounded above by the size of the input data and this fact may be unobvious without knowledge of some details of the entire implementation staircase mentioned above 1 . Nevertheless such a time-cost model is interesting from both theoretical and practical points of view.…”

Section: Introductionmentioning

confidence: 99%

“…Strings form a fundamental data type used in most programming languages. Recently, a number of techniques producing string constraints have been suggested for automatic testing [8,1] and program verification [16]. String-constraint solvers are used in many testing and analysis tools [5,2,6,15,23].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On Unfolding for Programs Using Strings as a Data Type

Nemytykh¹

EPiC Series in Computing

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As a rule, program transformation methods based on operational semantics unfold a semantic tree of a given program. Sometimes that allows ones to optimize the program or to automatically prove its certain properties. Unfolding is one of the basic operations, which is a meta-extension of one step of the abstract machine executing the program. This paper is interested in unfolding for programs based on pattern matching and manipulating the strings. The corresponding computation model originates with Markov's normal algorithms and extends this theoretical base. Even though algorithms unfolding programs were being intensively studied for a long time in the context of variety of programming languages, as far as we know, the associative concatenation was stood at the wayside of the stream. We define a class of term rewriting systems manipulating with strings and describe an algorithm unfolding the programs from the class. The programming language defined by this class is Turing-complete. The pattern language of the program class in turn fixes a class of word equations. Given an equation from the class, one of the algorithms suggested in this paper results in a description of the corresponding solution set.

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Section: On Semantics Of the Pattern Matchingmentioning

confidence: 99%

Section: Inductive Stepmentioning

confidence: 99%

Section: Inductive Stepmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On Unfolding for Programs Using Strings as a Data Type

Nemytykh¹

EPiC Series in Computing

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Quadratic Word Equations with Length Constraints, Counter Systems, and Presburger Arithmetic with Divisibility

Lin

Majumdar

2018

Automated Technology for Verification and Analysis

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Word equations are a crucial element in the theoretical foundation of constraint solving over strings, which have received a lot of attention in recent years. A word equation relates two words over string variables and constants. Its solution amounts to a function mapping variables to constant strings that equate the left and right hand sides of the equation. While the problem of solving word equations is decidable, the decidability of the problem of solving a word equation with a length constraint (i.e., a constraint relating the lengths of words in the word equation) has remained a long-standing open problem. In this paper, we focus on the subclass of quadratic word equations, i.e., in which each variable occurs at most twice. We first show that the length abstractions of solutions to quadratic word equations are in general not Presburger-definable. We then describe a class of counter systems with Presburger transition relations which capture the length abstraction of a quadratic word equation with regular constraints. We provide an encoding of the effect of a simple loop of the counter systems in the theory of existential Presburger Arithmetic with divisibility (PAD). Since PAD is decidable, we get a decision procedure for quadratic words equations with length constraints for which the associated counter system is flat (i.e., all nodes belong to at most one cycle). We show a decidability result (in fact, also an NP algorithm with a PAD oracle) for a recently proposed NP-complete fragment of word equations called regular-oriented word equations, together with length constraints. Decidability holds when the constraints are additionally extended with regular constraints with a 1-weak control structure.

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A Decision Procedure for String Logic with Quadratic Equations, Regular Expressions and Length Constraints

2018

Programming Languages and Systems

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In this work, we consider the satisfiability problem in a logic that combines word equations over string variables denoting words of unbounded lengths, regular languages to which words belong and Presburger constraints on the length of words. We present a novel decision procedure over two decidable fragments that include quadratic word equations (i.e., each string variable occurs at most twice). The proposed procedure reduces the problem to solving the satisfiability in the Presburger arithmetic. The procedure combines two main components: (i) an algorithm to derive a complete set of all solutions of conjunctions of word equations and regular expressions; and (ii) two methods to precisely compute relational constraints over string lengths implied by the set of all solutions. We have implemented a prototype tool and evaluated it over a set of satisfiability problems in the logic. The experimental results show that the tool is effective and efficient.Concrete string models assume a finite alphabet Σ whose elements are called letters, set of finite words over Σ * including ǫ -the empty word, and a set of integer numbers Z. We

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Path Feasibility Analysis for String-Manipulating Programs

Cited by 142 publications

References 20 publications

On Unfolding for Programs Using Strings as a Data Type

On Unfolding for Programs Using Strings as a Data Type

Quadratic Word Equations with Length Constraints, Counter Systems, and Presburger Arithmetic with Divisibility

A Decision Procedure for String Logic with Quadratic Equations, Regular Expressions and Length Constraints

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