TY - CHAP

T1 - Typeness for ω-regular automata

AU - Kupferman, Orna

AU - Morgenstern, Gila

AU - Murano, Aniello

PY - 2004

Y1 - 2004

N2 - We introduce and study three notions of typeness for automata on infinite words. For an acceptance-condition class 7 (that is, 7 is weak, Büchi, coBüchi, Rabin, or Streett), deterministic γ-typeness asks for the existence of an equivalent γ-automaton on the same deterministic structure, nondeterministic γ-typeness asks for the existence of an equivalent γ-automaton on the same structure, and γ-powerset- typeness asks for the existence of an equivalent γ-automaton on the (deterministic) powerset structure - one obtained by applying the subset construction. The notions are helpful in studying the complexity and complication of translations between the various classes of automata. For example, we prove that deterministic Büchi automata are co-Büchi type; it follows that a translation from deterministic Büchi to deterministic co-Büchi automata, when exists, involves no blow up. On the other hand, we prove that nondeterministic Büchi automata are not co-Büchi type; it follows that a translation from a nondeterministic Büchi to nondeterministic co-Büchi automata, when exists, should be more complicated than just redefining the acceptance condition. As a third example, by proving that nondeterministic co-Büchi automata are Büchi-powerset type, we show that a translation of nondeterministic co-Büchi to deterministic Büchi automata, when exists, can be done applying the subset construction. We give a complete picture of typeness for the weak, Büchi, co-Büchi, Rabin, and Streett acceptance conditions, and discuss its usefulness.

AB - We introduce and study three notions of typeness for automata on infinite words. For an acceptance-condition class 7 (that is, 7 is weak, Büchi, coBüchi, Rabin, or Streett), deterministic γ-typeness asks for the existence of an equivalent γ-automaton on the same deterministic structure, nondeterministic γ-typeness asks for the existence of an equivalent γ-automaton on the same structure, and γ-powerset- typeness asks for the existence of an equivalent γ-automaton on the (deterministic) powerset structure - one obtained by applying the subset construction. The notions are helpful in studying the complexity and complication of translations between the various classes of automata. For example, we prove that deterministic Büchi automata are co-Büchi type; it follows that a translation from deterministic Büchi to deterministic co-Büchi automata, when exists, involves no blow up. On the other hand, we prove that nondeterministic Büchi automata are not co-Büchi type; it follows that a translation from a nondeterministic Büchi to nondeterministic co-Büchi automata, when exists, should be more complicated than just redefining the acceptance condition. As a third example, by proving that nondeterministic co-Büchi automata are Büchi-powerset type, we show that a translation of nondeterministic co-Büchi to deterministic Büchi automata, when exists, can be done applying the subset construction. We give a complete picture of typeness for the weak, Büchi, co-Büchi, Rabin, and Streett acceptance conditions, and discuss its usefulness.

UR - http://www.scopus.com/inward/record.url?scp=35048848669&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-30476-0_27

DO - 10.1007/978-3-540-30476-0_27

M3 - Chapter

AN - SCOPUS:35048848669

SN - 9783540236108

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 324

EP - 338

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

A2 - Wang, Farn

PB - Springer Verlag

ER -