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Residual finite state automata (2002)
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BibTeX
@MISC{Denis02residualfinite,
author = {François Denis and Aurélien Lemay and Alain Terlutte},
title = {Residual finite state automata},
year = {2002}
}
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Abstract
We define a new variety of Non Deterministic Automata: a Residual Finite State Automata is a NFA all the states of which define residual languages of the language it recognizes. We prove that every regular language is recognized by a unique (canonical) RFSA which has a minimal number of states and a maximal number of transitions. Canonical RFSA are based on the notion of prime residual languages, i.e. that are not the union of other residual languages. We provide an algorithmic construction of the canonical RFSA from a given NFA. We study the size of canonical RFSA and the complexity of our constructions.
