Elsevier

Theoretical Computer Science

Volume 605, 9 November 2015, Pages 62-79
Theoretical Computer Science

Closure properties and complexity of rational sets of regular languages

https://doi.org/10.1016/j.tcs.2015.08.035Get rights and content
Under an Elsevier user license
open archive

Highlights

  • We settle most closure properties of rational sets of regular languages.

  • We prove complexity results for equivalence, inclusion, and membership checking.

  • We provide a systematic theoretical foundation for test coverage specifications.

Abstract

The test specification language FQL describes relevant test goals as regular expressions over program locations, such that each matching test case has an execution path matching this expression. To specify not only test goals but entire suites, FQL describes families of related test goals by regular expressions over extended alphabets: Herein, each symbol corresponds to a regular expression over program locations, and thus, a word in an FQL expression corresponds to a regular expression describing a single test goal. In this paper we provide a systematic foundation for FQL test specifications, which are in fact rational sets of regular languages (RSRLs). To address practically relevant problems like query optimization, we tackle open questions about RSRLs: We settle closure properties of general and finite RSRLs under common set theoretic operations. We also prove complexity results for checking equivalence and inclusion of star-free RSRLs, and for deciding whether a regular language is a member of a general or star-free RSRL.

Keywords

Rational sets
Regular languages
Test specification in FQL
Closure properties
Decision problems

Cited by (0)

1

Now at University of Toronto.

2

Now at Google London.