Temporal determinization of mutating finite automata: Reconstructing or restructuring

Abstract

Summary A mutating finite automaton (MFA) is a nondeterministic finite automaton (NFA) that changes its morphology over discrete time by a sequence of mutations. This results in a sequence of NFAs, the initial NFA, and one mutated NFA for each mutation. Some application domains, including model‐based diagnosis of discrete‐event systems in artificial intelligence and model‐based testing in software engineering, require temporal determinization of MFAs. Determinizing an MFA temporally means generating a deterministic finite automaton (DFA) that is equivalent to the mutated NFA as soon as a mutation occurs. Since, in computation time, the classical Subset Construction determinization algorithm may be less than optimal when applied to MFAs, a conservative algorithm is proposed, called Subset Restructuring, which, instead of constructing the new DFA from scratch based on the mutated NFA, generates the new DFA by updating the previous DFA based on the mutation occurred. Subset Restructuring is sound and complete, thereby yielding the same DFA generated by Subset Construction. Results from massive experimentation indicate the viability of Subset Restructuring, especially so when large MFAs change by small mutations.

Quick Subset Construction

“…Quick Subset Construction was not conceived overnight: it is the result of a series of algorithms designed for a specific research domain of artificial intelligence named model‐based diagnosis 2 . Specifically, the problem of incremental determinization of finite automata was addressed in monitoring‐based diagnosis of active systems, 3 which requires the incremental determinization of an NFA that changes over time 4‐7 …”

“…To our knowledge, in the literature there is no inward‐oriented determinization algorithm. Indeed, starting from Subset Construction , all the alternative determinization algorithms are invariably outward‐oriented, where the equivalent DFA is generated from scratch.Perhaps, in this respect, the closest algorithm to Quick Subset Construction is Subset Restructuring , 7 which was designed for the determinization of mutating automata. A mutating finite automaton is an NFA that changes its morphology over discrete time by a sequence of mutations , where a mutation causes some changes in the transition function of an NFA, such as the insertion and/or removal of some transitions as well as involved states.…”

“…2 Specifically, the problem of incremental determinization of finite automata was addressed in monitoring-based diagnosis of active systems, 3 which requires the incremental determinization of an NFA that changes over time. [4][5][6][7] To our knowledge, in the literature there is no inward-oriented determinization algorithm. Indeed, starting from Subset Construction, all the alternative determinization algorithms are invariably outward-oriented, where the equivalent DFA is generated from scratch.…”