ω-automaton

About: ω-automaton is a research topic. Over the lifetime, 2299 publications have been published within this topic receiving 68468 citations. The topic is also known as: stream automaton & ω-automata.

On Information Lossless Automata of Finite Order

Abstract: A coding graph is a model which contains all the types of finite automata and codes as special cases. A test for information losslessness and for information losslessness of finite order of a coding graph is described. Efficient methods of computation are given which make the calculation simple and mechanizable. The application of the tests to finite deterministic automata is discussed and a method of constructing a decoder for a given finite automaton that is information lossless of finite order, is described.

Minimal cover-automata for finite languages

Abstract: A cover-automaton A of a finite language L ⊆ Σ * is a finite automaton that accepts all words in L and possibly other words that are longer than any word in L. A minimal deterministic cover automaton of a finite language L usually has a smaller size than a minimal DFA that accept L. Thus, cover automata can be used to reduce the size of the representations of finite languages in practice. In this paper, we describe an efficient algorithm that, for a given DFA accepting a finite language, constructs a minimal deterministic finite cover- automaton of the language. We also give algorithms for the boolean operations on deterministic cover automata, i.e., on the finite languages they represent.

Alternating weighted automata

Abstract: Weighted automata are finite automata with numerical weights on transitions. Nondeterministic weighted automata define quantitative languages L that assign to each word w a real number L(w) computed as the maximal value of all runs over w, and the value of a run r is a function of the sequence of weights that appear along r. There are several natural functions to consider such as Sup, LimSup, LimInf, limit average, and discounted sum of transition weights. We introduce alternating weighted automata in which the transitions of the runs are chosen by two players in a turn-based fashion. Each word is assigned the maximal value of a run that the first player can enforce regardless of the choices made by the second player. We survey the results about closure properties, expressiveness, and decision problems for nondeterministic weighted automata, and we extend these results to alternating weighted automata. For quantitative languages L1 and L2, we consider the pointwise operations max(L1, L2), min(L1, L2), 1 - L1, and the sum L1 + L2. We establish the closure properties of all classes of alternating weighted automata with respect to these four operations. We next compare the expressive power of the various classes of alternating and nondeterministic weighted automata over infinite words. In particular, for limit average and discounted sum, we show that alternation brings more expressive power than nondeterminism. Finally, we present decidability results and open questions for the quantitative extension of the classical decision problems in automata theory: emptiness, universality, language inclusion, and language equivalence.

Optimal Bounds for Transformations of omega-Automata

Abstract: In this paper we settle the complexity of some basic constructions of ω-automata theory, concerning transformations of automata characterizing the set of ω-regular languages. In particular we consider Safra's construction (for the conversion of nondeterministic Buchi automata into deterministic Rabin automata) and the appearance record constructions (for the transformation between different models of deterministic automata with various acceptance conditions). Extending results of Michel (1988) and Dziembowski, Jurdzinski, and Walukiewicz (1997), we obtain sharplo wer bounds on the size of the constructed automata.