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.

Yet another proof of the cascade decomposition theorem for finite automata: Correction

Abstract: Dr. Jurg Nievergelt of the University of Illinois has pointed out that Method II can be blocked in a way not covered in lines 9 and 10 of page 227 (Math. Systems Theory 1 (1967), 225-228): if sgrp A consists entirely of permutations and resets, then T will be the ideal of resets and V the group of units; Method II will then produce a first component that is permutation-reset, and hence no simpler than the original automaton. To salvage the proof we eliminate the resets from this first component by modifying the method as follows: Let st B1 = V instead of T, then whenever u is in T, let p' = p (instead of u), and r' = p-1 (the state to which u resets), instead of p(r). This method (call it IIA) then suffices to decompose a permutationreset automaton into a permutation automaton followed by a reset automaton; since the methods as originally stated bring an arbitrary automaton to a cascade of permutation-reset automata, Method IIA finishes the job.

Controlled finite automata

Abstract: This paper discusses finite automata regulated by control languages over their states and transition rules. It proves that under both regulations, regular-controlled finite automata and context-free-controlled finite automata characterize the family of regular languages and the family of context-free languages, respectively. It also establishes conditions under which any state-controlled finite automaton can be turned into an equivalent transition-controlled finite automaton and vice versa. The paper also demonstrates a close relation between these automata and programmed grammars. Indeed, it proves that finite automata controlled by languages generated by propagating programmed grammars with appearance checking are computationally complete. In fact, it demonstrates that this computational completeness holds even in terms of these automata with a reduced number of states.

Quantum finite state automata over infinite words

Abstract: The study of finite state automata working on infinite words was initiated by Buchi [1]. Buchi discovered connection between formulas of the monadic second order logic of infinite sequences (S1S) and ω-regular languages, the class of languages over infinite words accepted by finite state automata. Few years later, Muller proposed an alternative definition of finite automata on infinite words [4]. McNaughton proved that with Muller’s definition, deterministic automata recognize all ω-regular languages [2]. Later, Rabin extended decidability result of Buchi for S1S to the monadic second order of the infinite binary tree (S2S) [5]. Rabin theorem can be used to settle a number of decision problems in logic. A theory of automata over infinite words has started from these studies.

Quantum finite automata and weighted automata

Abstract: Quantum finite automata derive their strength by exploiting interference in complex valued probability amplitudes. Of particular interest is the 2-way model of Ambainis and Watrous that has both quantum and classical states (2QCFA) [A. Ambainis and J. Watrous, Two-way finite automata with quantum and classical state, Theoretical Computer Science, 287 (2002) 1, 299-311], since it combines the advantage of the power of interference in a constant-sized quantum system with a 2-way head. This paper is a step towards finding the least powerful model which is purely classical and can mimic the dynamics of quantum phase. We consider weighted automata with the Cortes-Mohri definition of language recognition [C. Cortes and M. Mohri, Context-Free Recognition with Weighted Automata, Grammars 3 (2000) 2/3, 133-150] as a candidate model for simulating 2QCFA. Given any 2QCFA that (i) uses the accept-reject-continue observable, (ii) recognizes a language with one-sided error and (iii) the entries of whose unitary matrices are algebraic complex numbers, we show a method of constructing a weighted automaton over C that simulates it efficiently.