Title
On the Structure and Complexity of Rational Sets of Regular Languages
Abstract
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.
Year
DOI
Venue
2013
10.4230/LIPIcs.FSTTCS.2013.377
FSTTCS
DocType
Volume
Citations 
Journal
abs/1305.6074
2
PageRank 
References 
Authors
0.36
13
4
Name
Order
Citations
PageRank
Andreas Holzer119713.62
Christian Schallhart2113756.06
Michael Tautschnig342525.84
Helmut Veith42476140.58