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.

Simulation of systolic tree automata on trellis automata

Abstract: The relation between two basic types of systolic automata—tree automata and trellis automata—is investigated. First it is shown that for every natural t>1 there is a simple nonhomogeneous (actually regular and also modular) trellis such that any t-ary systolic tree automaton can be simulated in a universal and quite straighforward way on a trellis automaton over . This implies that the family of languages accepted by systolic tree automata, which is incomparable with the family of languages accepted by homogeneous systolic trellis automata, is actually contained in the family of languages accepted by trellis automata that are both regular and modular.

Reversible Ordered Restarting Automata

Abstract: Stateless deterministic ordered restarting automata characterize the class of regular languages. Here we introduce a notion of reversibility for these automata and show that each regular language is accepted by such a reversible stateless deterministic ordered restarting automaton. We study the descriptional complexity of these automata, showing that they are exponentially more succinct than nondeterministic finite-state acceptors. We also look at the case of unary input alphabets.

One-way quantum finite automata together with classical states: Equivalence and Minimization

Abstract: One-way quantum finite automata (1QFA) proposed by Moore and Crutchfield and by Kondacs and Watrous accept only subsets of regular languages with bounded error. In this paper, we develop a new computing model of 1QFA, namely, one-way quantum finite automata together with classical states (1QFAC for short). In this model, a component of classical states is added, and the choice of unitary evolution of quantum states at each step is closely related to the current classical state. 1QFAC can accept all regular languages with no error, and in particular, 1QFAC can accept some languages with essentially less number of states than deterministic finite automata (DFA). The main technical results are as follows. (1) We prove that the set of languages accepted by 1QFAC with bounded error consists precisely of all regular languages. (2) We show that, for any prime number m ≥ 2, there exists a regular language L0(m) whose minimal DFA needs O(m) states and that can not be accepted by the 1QFA proposed by Moore and Crutchfield and by Kondacs and Watrous, but there exists 1QFAC accepting L0(m) with only constant classical states and O(log(m)) quantum basis states. Analogous results for multi-letter automata are also established. (3) By a bilinearization technique we prove that any two 1QFAC A1 and A2 are equivalent if and only if they are (k1n1) 2 + (k2n2) 2 − 1-equivalent, and there exists a polynomial-time O([(k1n1) 2 + (k2n2) 2]4) algorithm for determining their equivalence, where k1 and k2 are the numbers of classical states of A1 and A2, as well as n1 and n2 are the numbers of quantum basis states of A1 andA2, respectively. (4) We show that the minimization problem of 1QFAC is in EXPSPACE. As a corollary of this result, we obtain that the minimization problem of MO-1QFA is also in EXPSPACE. Finally, we draw some conclusions and point out open ∗Corresponding author. E-mail address: issqdw@mail.sysu.edu.cn (D. Qiu). †E-mail address: {paulo.mateus,amilcar.sernadas}@math.ist.utl.pt.