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.

Perfect Hashing with Pseudo-minimal Bottom-up Deterministic Tree Automata

Abstract: We describe a technique that maps unranked trees to their hash codes using a bottom-up deterministic tree automaton (DTA). In contrast to techniques implemented with minimal tree automata, our procedure builds a pseudo-minimal DTA. Pseudo-minimal automata are larger than the minimal ones but in turn the mapping can be arbitrary, so it can be determined prior to the automaton construction. We also provide procedures to build incrementally the pseudo-minimal DTA and the associated hash codes.

Method of reducing finite controlling automata and corresponding computer-readable medium

Abstract: When the automatic controls of a number of small automata are synthesized to form large automata, the latter are often difficult to manipulate and for the most part cannot be represented graphically In order to maintain the applicability of incremental verification techniques, the larger automata are reduced, in accordance with the invention This is done by modeling the automata in a discrete event system DES and by eliminating from the DES all redundant state transitions, disallowed states, and unimportant selfloops The novel method is most prominently applicable in control programs and distributed control system controllers

Directly Constructing Minimal DFAs: Combining Two Algorithms by Brzozowski

Abstract: In this paper, we combine (and refine) two of Brzozowski's algorithms -- yielding a single algorithm which constructs a minimal deterministic finite automaton (DFA) from a regular expression.

Exponentially more concise quantum recognition of non-RMM regular languages

Abstract: We show that there are quantum devices that accept all regular languages and that are exponentially more concise than deterministic finite automata (DFA). For this purpose, we introduce a new computing model of {\it one-way quantum finite automata} (1QFA), namely, {\it one-way quantum finite automata together with classical states} (1QFAC), which extends naturally both measure-only 1QFA and DFA and whose state complexity is upper-bounded by both. The original contributions of the paper are the following. First, we show that the set of languages accepted by 1QFAC with bounded error consists precisely of all regular languages. Second, we prove that 1QFAC are at most exponentially more concise than DFA. Third, we show that the previous bound is tight for families of regular languages that are not recognized by measure-once (RMO), measure-many (RMM) and multi-letter 1QFA. % More concretely we exhibit regular languages $L^0(m)$ for $m$ prime such that: (i) $L^0(m)$ cannot be recognized by measure-once, measure-many and multi-letter 1QFA; (ii) the minimal DFA that accepts $L^0(m)$ has $O(m)$ states; (iii) there is a 1QFAC with constant classical states and $O(\log(m))$ quantum basis that accepts $L^0(m)$. Fourth, we give a polynomial-time algorithm for determining whether any two 1QFAC are equivalent. Finally, we show that state minimization of 1QFAC is decidable within EXPSPACE. We conclude the paper by posing some open problems.