Detecting Fictitious States in a Σ-Automaton Synthesized from Its Specification in the Language LP
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Synthesizing a deterministic Σ-automaton specified in the language LP consists in sequentially executing two procedures. The first constructs an automaton with a subautomaton identical to the automaton specified, and the other eliminates the states that do not belong to this subautomaton. Such states are called fictitious. A method for detecting fictitious states is considered. The obtained results allow to reduce the detection of fictitious states to finding the so-called basic cycles and eventually to checking the membership of a periodic left-infinite word in some –ω-regular set.
KeywordsΣ-automaton fictitious state initial strongly connected subautomaton normal form –ω-regular set basic cycle
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