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.

Diversity-Based Inference of Finite Automata (Extended Abstract)

Abstract: We present a new procedure for inferring the structure of a finitestate automaton (FSA) from its input/output behavior, using access to the automaton to perform experiments. Our procedure uses a new representation for FSA's, based on the notion of equivalence between testa. We call the number of such equivalence classes the diversity of the automaton; the diversity may be as small as the logarithm of the number of states of the automaton. The size of our representation of the FSA, and the running time of our procedure (in some case provably, in others conjecturally) is polynomial in the diversity and ln(1/e), where e is a given upper bound on the probability that our procedure returns an incorrect result. (Since our procedure uses randomization to perform experiments, there is a certain controllable chance that it will return an erroneous result.) We also present some evidence for the practical efficiency of our approach. For example, our procedure is able to infer the structure of an automaton based on Rubik's Cube (which has approximately 1019 states) in about 2 minutes on a DEC Micro Vax. This automaton is many orders of magnitude larger than possible with previous techniques, which would require time proportional at least to the number of global states. (Note that in this example, only a small fraction (10-14) of the global states were even visited.)

Complementing Semi-deterministic Büchi Automata

Abstract: We introduce an efficient complementation technique for semi-deterministic Buchi automata, which are Buchi automata that are deterministic in the limit: from every accepting state onward, their behaviour is deterministic. It is interesting to study semi-deterministic automata, because they play a role in practical applications of automata theory, such as the analysis of Markov decision processes. Our motivation to study their complementation comes from the termination analysis implemented in Ultimate Buchi Automizer, where these automata represent checked runs and have to be complemented to identify runs to be checked. We show that semi-determinism leads to a simpler complementation procedure: an extended breakpoint construction that allows for symbolic implementation. It also leads to significantly improved bounds as the complement of a semi-deterministic automaton with n states has less than $$4^n$$ states. Moreover, the resulting automaton is unambiguous, which again offers new applications, like the analysis of Markov chains. We have evaluated our construction against the semi-deterministic automata produced by the Ultimate Buchi Automizer. The evaluation confirms that our algorithm outperforms the known complementation techniques for general nondeterministic Buchi automata.

Problems on Finite Automata and the Exponential Time Hypothesis

Abstract: We study several classical decision problems on finite automata under the (Strong) Exponential Time Hypothesis. We focus on three types of problems: universality, equivalence, and emptiness of intersection. All these problems are known to be CoNP-hard for nondeterministic finite automata, even when restricted to unary input alphabets. A different type of problems on finite automata relates to aperiodicity and to synchronizing words. We also consider finite automata that work on commutative alphabets and those working on two-dimensional words.

On Zone-Based Analysis of Duration Probabilistic Automata

Abstract: We propose an extension of the zone-based algorithmics for analyzing timed automata to handle systems where timing uncertainty is considered as probabilistic rather than set-theoretic. We study duration probabilistic automata (DPA), expressing multiple parallel processes admitting memoryfull continuously-distributed durations. For this model we develop an extension of the zone-based forward reachability algorithm whose successor operator is a density transformer, thus providing a solution to verification and performance evaluation problems concerning acyclic DPA (or the bounded-horizon behavior of cyclic DPA).

Describing periodicity in two-way deterministic finite automata using transformation semigroups

Abstract: A framework for the study of periodic behaviour of two-way deterministic finite automata (2DFA) is developed. Computations of 2DFAs are represented by a two-way analogue of transformation semigroups, every element of which describes the behaviour of a 2DFA on a certain string x. A subsemigroup generated by this element represents the behaviour on strings in x+. The main contribution of this paper is a description of all such monogenic subsemigroups up to isomorphism. This characterization is then used to show that transforming an n-state 2DFA over a one-letter alphabet to an equivalent sweeping 2DFA requires exactly n+1 states, and transforming it to a one-way automaton requires exactly max0≤l≤n G(n - l) + l + 1 states, where G(k) is the maximum order of a permutation of k elements.