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• W4384302160 abstract "We revisit the membership problem for subclasses of rational relations over finite and infinite words: Given a relation R in a class C <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</inf> , does R belong to a smaller class C <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</inf> ? The subclasses of rational relations that we consider are formed by the deterministic rational relations, synchronous (also called automatic or regular) relations, and recognizable relations. For almost all versions of the membership problem, determining the precise complexity or even decidability has remained an open problem for almost two decades. In this paper, we provide improved complexity and new decidability results. (i) Testing whether a synchronous relation over infinite words is recognizable is NL-complete (PSPACE-complete) if the relation is given by a deterministic (nondeterministic) ω-automaton. This fully settles the complexity of this recognizability problem, matching the complexity of the same problem over finite words. (ii) Testing whether a deterministic rational binary relation is recognizable is decidable in polynomial time, which improves a previously known double exponential time upper bound. For relations of higher arity, we present a randomized exponential time algorithm. (iii) We provide the first algorithm to decide whether a deterministic rational relation is synchronous. For binary relations the algorithm even runs in polynomial time." @default.
• W4384302160 created "2023-07-15" @default.
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• W4384302160 date "2023-06-26" @default.
• W4384302160 modified "2023-10-17" @default.
• W4384302160 title "Revisiting Membership Problems in Subclasses of Rational Relations" @default.
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• W4384302160 doi "https://doi.org/10.1109/lics56636.2023.10175722" @default.
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