Membership and Finiteness Problems for Rational Sets of Regular Languages

Afonin, Sergey; Hazova, Elena

doi:10.1007/11505877_8

Cited by 4 publications

(11 citation statements)

References 17 publications

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“…Quoted regular expressions were previously introduced in the literature by Afonin et al [9] under the name rational sets of regular languages (RSRLs). In query-driven program testing, RSRLs have a similar role for test specifications as relational algebra has for databases.…”

Section: ) Specification Of Coverage Criteria By Quoted Regularmentioning

confidence: 99%

Perspectives on White-Box Testing: Coverage, Concurrency, and Concolic Execution

Farzan

Holzer

Veith

2015

2015 IEEE 8th International Conference on Software Testing, Verification and Validation (ICST)

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The last years have seen a fruitful exchange of ideas between automated software verification and white-box software testing; the industrial impact of concolic testing for sequential software is the most notable result of this interdisciplinary effort. While concolic testing is very successful at finding bugs, and even achieves verification in the limit, it is often hard to quantify the progress it achieves towards verification. In this paper, we survey two recent projects which aim to remedy this situation: In the FQL project, we devise a test specification language which facilitates precise specification of coverage criteria, and a separation of concerns between test specification and test case generation. In con2colic testing, we develop a concolic testing methodology for concurrent programs where progress is measured in terms of the data flow between program threads.

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Section: ) Specification Of Coverage Criteria By Quoted Regularmentioning

confidence: 99%

Perspectives on White-Box Testing: Coverage, Concurrency, and Concolic Execution

Farzan

Holzer

Veith

2015

2015 IEEE 8th International Conference on Software Testing, Verification and Validation (ICST)

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“…Afonin et al [8] introduced RSRL and studied the decidability of whether a regular language is contained in an RSRL and the decidability of whether an RSRL is finite. Although Afonin et al shortly discuss possible upper bounds for the membership decision problem, their analysis is incomplete due to gaps in their algorithmic presentation.…”

Section: Related Workmentioning

confidence: 99%

“…In the general case, the situation is quite different: Previous work shows that the membership problem is decidable [8]. Taking this work as starting point, we give a first 2ExpSpace upper bound on the complexity of the problem.…”

Section: Decision Problemsmentioning

confidence: 99%

“…The property we exploit is given by the following proposition. Theorem 27 (Membership Condition, following [8]). Let R = (K, ϕ) be a RSRL and ϕ : ∆ → 2 Σ ⋆ be a regular language substitution.…”

Section: Membership For General Rsrlsmentioning

confidence: 99%

“…Each of these words is a regular expression that will then serve as a test goal. Following [8], we call such languages rational sets of regular languages (RSRL).…”

Section: Introductionmentioning

confidence: 99%

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Closure properties and complexity of rational sets of regular languages

Holzer

Schallhart

Tautschnig

et al. 2015

Theoretical Computer Science

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In a recent thread of papers, we have introduced FQL, a precise specification language for test coverage, and developed the test case generation engine Fshell for ANSI C. In essence, an FQL test specification amounts to a set of regular languages, each of which has to be matched by at least one test execution. To describe such sets of regular languages, the FQL semantics uses an automata-theoretic concept known as rational sets of regular languages (RSRLs). RSRLs are automata whose alphabet consists of regular expressions. Thus, the language accepted by the automaton is a set of regular expressions. In this paper, we study RSRLs from a theoretic point of view. More specifically, we analyze RSRL closure properties under common set theoretic operations, and the complexity of membership checking, i.e., whether a regular language is an element of a RSRL. For all questions we investigate both the general case and the case of finite sets of regular languages. Although a few properties are left as open problems, the paper provides a systematic semantic foundation for the test specification language FQL.

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A Note on Finitely Generated Semigroups of Regular Languages

Afonin

Khazova²

2007

Semigroups and Formal Languages

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Let E = {E 1 ,. .. , E k } be a set of regular languages over a finite alphabet Σ. Consider morphism ϕ : ∆ + → (S, •) where ∆ + is the semigroup over a finite set ∆ and (S, •) = E is the finitely generated semigroup with E as the set of generators and language concatenation as a product. We prove that the membership problem of the semigroup S, the set [u] = {v ∈ ∆ + | ϕ(v) = ϕ(u)}, is a regular language over ∆, while the set Ker(ϕ) = {(u, v) | u, v ∈ ∆ + ϕ(u) = ϕ(v)} need not to be regular. It is conjectured however that every semigroup of regular languages is automatic.

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Membership and Finiteness Problems for Rational Sets of Regular Languages

Cited by 4 publications

References 17 publications

Perspectives on White-Box Testing: Coverage, Concurrency, and Concolic Execution

Perspectives on White-Box Testing: Coverage, Concurrency, and Concolic Execution

Closure properties and complexity of rational sets of regular languages

A Note on Finitely Generated Semigroups of Regular Languages

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