Mutation of Directed Graphs -- Corresponding Regular Expressions and Complexity of Their Generation

TL;DR

This paper investigates how manipulating directed graphs, representing finite-state automata, affects their equivalent regular expressions, focusing on the complexity of generating these expressions and implications for mutation testing.

Contribution

It introduces a systematic analysis of graph mutations and their impact on corresponding regular expressions, highlighting potential benefits for mutation testing in complex systems.

Findings

Graph manipulations can produce diverse mutants of DG and RE.

Switching to RE can simplify modeling of complex systems.

The study provides insights into the complexity of generating RE from DG mutations.

Abstract

Directed graphs (DG), interpreted as state transition diagrams, are traditionally used to represent finite-state automata (FSA). In the context of formal languages, both FSA and regular expressions (RE) are equivalent in that they accept and generate, respectively, type-3 (regular) languages. Based on our previous work, this paper analyzes effects of graph manipulations on corresponding RE. In this present, starting stage we assume that the DG under consideration contains no cycles. Graph manipulation is performed by deleting or inserting of nodes or arcs. Combined and/or multiple application of these basic operators enable a great variety of transformations of DG (and corresponding RE) that can be seen as mutants of the original DG (and corresponding RE). DG are popular for modeling complex systems; however they easily become intractable if the system under consideration is complex and/or large. In such situations, we propose to switch to corresponding RE in order to benefit from their compact format for modeling and algebraic operations for analysis. The results of the study are of great potential interest to mutation testing.