Conservative Determinization of Translated Automata by Embedded Subset Construction

Abstract

A translated finite automaton (TFA) results from a translation of a deterministic finite automaton (DFA). A translation is based on a mapping from the alphabet of the DFA to a new alphabet, where each symbol in the original alphabet is substituted with a symbol in the new alphabet. When this substitution generates a nondeterministic automaton, the TFA may need to be determinized into an equivalent DFA. Determinization of TFAs may be useful in a variety of domains, specifically in model-based diagnosis of discrete-event systems, where large TFAs constructed by model-based reasoning are processed to perform knowledge compilation. Since, in computation time, the classical Subset Construction determinization algorithm may be less than optimal when applied to large TFAs, a conservative algorithm is proposed, called Embedded Subset Construction. This alternative algorithm updates the TFA based on the mapping of the alphabet rather than building a new DFA from scratch. This way, in contrast with Subset Construction, which performs an exhaustive processing of the TFA to be determinized, the portion of the TFA that does not require determinization is not processed. Embedded Subset Construction is sound and complete, thereby yielding a DFA that is identical to the DFA generated by Subset Construction. The benefit of using Embedded Subset Construction largely depends on the portion of the TFA that actually requires determinization. Experimental results indicate the viability of Embedded Subset Construction, especially so when large TFAs are affected by small portions of nondeterminism.