Determinization of Transducers over Infinite Words: The General Case

Determinization of transducers over finite and infinite words

Rankers over Infinite Words

We consider the fragments FO, Σ2 ∩ FO, Π2 ∩ FO, and ∆2 of first-order logic FO[<] over finite and infinite words. For all four fragments, we give characterizations in terms of rankers. In particular, we generalize the notion of a ranker to infinite words in two possible ways. Both extensions are natural in the sense that over finite words, they coincide with classical rankers and over infinite ...

Group Extensions over Infinite Words

We construct an extension E(A,G) of a given group G by infinite nonArchimedean words over an discretely ordered abelian group like Z. This yields an effective and uniform method to study various groups that ”behave like G”. We show that the Word Problem for f.g. subgroups in the extension is decidable if and only if and only if the Cyclic Membership Problem in G is decidable. The present paper ...

On the Expressiveness of Deterministic Transducers over Infinite Trees

We introduce top-down deterministic transducers with rational lookahead (transducer for short) working on infinite terms. We show that for such a transducer e T , there exists an MSO-transduction T such that for any graph G, unfold(T (G)) = e T (unfold(G)). Reciprocally, we show that if an MSO-transduction T “preserves bisimilarity”, then there is a transducer e T such that for any graph G, unf...

Probabilistic Acceptors for Languages over Infinite Words

Probabilistic ω-automata are variants of nondeterministic automata for infinite words where all choices are resolved by probabilistic distributions. Acceptance of an infinite input word requires that the probability for the accepting runs is positive. In this paper, we provide a summary of the fundamental properties of probabilistic ω-automata concerning expressiveness, efficiency, compositiona...