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.

The Implementation of Cellular Automata with Non-identical Rule on Serial Base

Abstract: A cellular automaton is a calculation method which strongly needs high-speed processing of data. In cellular automata, a very large volume of data must be processed in a short time, so that the results of cellular automata can be used. Different methods can be used to implement cellular automata, among which the implementation of cellular automata on serial bases is one of the simplest ones. Two types of implementing cellular automata on a serial base were studied in this paper. In a method of implementation, the whole cells of automata the use the same rule; and in another method, the rule related to cells is different depending on the location. Then, the speed of implementation of the two methods is compared: it was shown that the speed of operations in the serial implementation is independent of cellular automata rule.

Approximating deterministic lattice automata

Abstract: Traditional automata accept or reject their input, and are therefore Boolean. Lattice automata generalize the traditional setting and map words to values taken from a lattice. In particular, in a fully-ordered lattice, the elements are 0,1,…,n−1, ordered by the standard ≤ order. Lattice automata, and in particular lattice automata defined with respect to fully-ordered lattices, have interesting theoretical properties as well as applications in formal methods. Minimal deterministic automata capture the combinatorial nature and complexity of a formal language. Deterministic automata have many applications in practice. In [13], we studied minimization of deterministic lattice automata. We proved that the problem is in general NP-complete, yet can be solved in polynomial time in the case the lattices are fully-ordered. The multi-valued setting makes it possible to combine reasoning about lattice automata with approximation. An approximating automaton may map a word to a range of values that are close enough, under some pre-defined distance metric, to its exact value. We study the problem of finding minimal approximating deterministic lattice automata defined with respect to fully-ordered lattices. We consider approximation by absolute distance, where an exact value x can be mapped to values in the range [x−t,x+t], for an approximation factor t, as well as approximation by separation, where values are mapped into t classes. We prove that in both cases the problem is in general NP-complete, but point to special cases that can be solved in polynomial time.

Automata in algebra

Abstract: In this paper, some algebraic problems are considered. Several aspects of automaton theory and algebraic structures needed to obtain solutions of the problems are discussed.

On the Number of Transitions Entering the States of a Finite Automaton

Abstract: In recent years adaptive threshold ele-ments have been used as the basis for learning machines such as the Perceptron [1] and Adaline [2]. To the author's knowledge there has been no previously reported work on a systematic study of algorithms, used in learning machines, to modify the weightvalues of threshold elements.

Finite Automata, Real Time Processes and Counting Problems in Bounded Arithmetics

Abstract: In this paper we present a negative solution of counting problems for some classes slightly different from bounded arithmetic (,0 sets). To get the results we study properties of chains of finite automata. ?1. Basic definitions and discussion of the results. By finite automata we understand-one-way deterministic finite automata. We also assume that at each step of an execution finite automata move 1 position; they do not stop moving. Because of this assumption, if we employ several automata on the same input, they work synchronously and they read the same symbol at the same time. Because this works as in a real-time process we could refer to this symbol as to the current input signal. DEFINITION 1.1. (i) A k-automaton is a finite automaton using no more than k states. A p-counting automaton is a finite automaton with the states 0, 1,... , p 1 and the state transition function 6 such that for every state i and symbol x we have 6(x,i) = i + h(x)(modp), where h is a function associated with this automaton with rng h c {0, 1 }. Aut is a counting automaton if it is a p-counting automaton for some p. (ii) is a chain of finite automata iff the automata Autl,.. ., Autt have one common reading head moving to the left without stopping and for each j is a k-chain if Aut1,... , Autt are k-automata, i.e. IQ I = = IQtI = k. is a chain of k-automata and counting automata if for Received September 11, 1985; revised January 30, 1987. ? 1988, Association for Symbolic Logic 0022-4812/88/5301 -0020/$02.60