Topic
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.
Papers published on a yearly basis
Papers
More filters
TL;DR: The main result is that inequality of rational weight finite automata with finite behaviors is in R, random polynomial time.
24 May 2023
TL;DR: In the context of finite words, semantic determinism coincides with determinism, in the sense that every pruning of an SD automaton to a deterministic one results in an equivalent automaton as mentioned in this paper .
Abstract: A nondeterministic automaton is semantically deterministic (SD) if different nondeterministic choices in the automaton lead to equivalent states. Semantic determinism is interesting as it is a natural relaxation of determinism, and as some applications of deterministic automata in formal methods can actually use automata with some level of nondeterminism, tightly related to semantic determinism. In the context of finite words, semantic determinism coincides with determinism, in the sense that every pruning of an SD automaton to a deterministic one results in an equivalent automaton. We study SD automata on infinite words, focusing on B\"uchi, co-B\"uchi, and weak automata. We show that there, while semantic determinism does not increase the expressive power, the combinatorial and computational properties of SD automata are very different from these of deterministic automata. In particular, SD B\"uchi and co-B\"uchi automata are exponentially more succinct than deterministic ones (in fact, also exponentially more succinct than history-deterministic automata), their complementation involves an exponential blow up, and decision procedures for them like universality and minimization are PSPACE-complete. For weak automata, we show that while an SD weak automaton need not be pruned to an equivalent deterministic one, it can be determinized to an equivalent deterministic weak automaton with the same state space, implying also efficient complementation and decision procedures for SD weak automata.
10 Jan 2023
TL;DR: ALMA as discussed by the authors is a Java-based tool that can learn any automaton accepting regular languages of finite or infinite words with an implementable membership query function, and it can test whether a word is accepted by performing a membership query on the learned automaton.
Abstract: We present ALMA (Automata Learner using modulo 2 Multiplicity Automata), a Java-based tool that can learn any automaton accepting regular languages of finite or infinite words with an implementable membership query function. Users can either pass as input their own membership query function, or use the predefined membership query functions for modulo 2 multiplicity automata and non-deterministic B\"uchi automata. While learning, ALMA can output the state of the observation table after every equivalence query, and upon termination, it can output the dimension, transition matrices, and final vector of the learned modulo 2 multiplicity automaton. Users can test whether a word is accepted by performing a membership query on the learned automaton. ALMA follows the polynomial-time learning algorithm of Beimel et. al. (Learning functions represented as multiplicity automata. J. ACM 47(3), 2000), which uses membership and equivalence queries and represents hypotheses using modulo 2 multiplicity automata. ALMA also implements a polynomial-time learning algorithm for strongly unambiguous B\"uchi automata by Angluin et. al. (Strongly unambiguous B\"uchi automata are polynomially predictable with membership queries. CSL 2020), and a minimization algorithm for modulo 2 multiplicity automata by Sakarovitch (Elements of Automata Theory. 2009).
01 Jan 2022
Journal Article•
TL;DR: In this article, the authors consider the problem of enumeration of Muller automata with a given number of states and show that the acceptance table of a Muller Automata is admissible if, for each element f E F, there exists an infinite word whose set of states visited infinitely often is exactly f.
Abstract: In this paper, we consider the problem of enumeration of Muller automata with a given number of states. Given a Muller automata, its acceptance table F is admissible if, for each element f E F, there exists an infinite word whose set of states visited infinitely often is exactly f. We consider acceptance tables in Muller automata which are never admissible, regardless of the choice of transition function δ. We apply the results to enumeration of Muller automata by number of states.