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Showing papers on "ω-automaton published in 1986"


Journal ArticleDOI
TL;DR: The main theorem allows an elegant algorithm to be refined into an efficient one based on ‘marking of’ regular expressions based on derivatives of regular expressions, which constructs an automaton for the marked expression.

311 citations


Journal ArticleDOI
01 Mar 1986
TL;DR: It is proven that 1) discretized two-action linear reward-inaction automata are absorbing and ¿-optimal in all environments; 2)DiscretizedTwo- action linear inaction-penalty learning automata with artificially created absorbing barriers are ergodic and expedient inAll environments.
Abstract: A learning automaton is a machine that interacts with a random environment and that simultaneously learns the optimal action that the environment offers to it Learning automata with variable structure are considered Such automata are completely defined by a set of probability updating rules Contrary to all the variable-structure stochastic automata (VSSA) discussed in the literature, which update the probabilities in such a way that an action probability can take any real value in the interval [0,1], the probability space is discretized so as to permit the action probability to assume one of a finite number of distinct values in [0,1] The discretized automaton is termed linear or nonlinear depending on whether the subintervals of [0,1] are of equal length It is proven that 1) discretized two-action linear reward-inaction automata are absorbing and ?-optimal in all environments; 2) discretized two-action linear inaction-penalty automata are ergodic and expedient in all environments; 3) discretized two-action linear inaction-penalty learning automata with artificially created absorbing barriers are ?-optimal in all random environments; and 4) there exist nonlinear discretized reward-inaction automata that are ?-optimal in all random environments The maximum advantage gained by rendering any finite-state discretized automaton nonlinear has also been derived

112 citations


Journal ArticleDOI
TL;DR: It follows from them that there exist exactly a countably infinite number of self-affine functions modulo constant multiplications.
Abstract: A characterization of self-affine functions as functions generated by finite automata is given. Also, a kind of uniqueness in representing a self-affine function by a finite automaton is proved. It follows from them that there exist exactly a countably infinite number of self-affine functions modulo constant multiplications.

34 citations


Journal ArticleDOI
TL;DR: It is shown that the parallel evolution of a network of automata N can be sequentially simulated by another network N′ whose local transition functions are the same as those of N.

20 citations



Journal ArticleDOI
01 Jul 1986
TL;DR: The automata used in this solution are the Absorbing discretized linear Inaction-Penalty (ADLIP) automata, which are the only known linear automata which are of an inaction-penalty type and yet asymptotically optimal.
Abstract: The minimum-spanning circle (MSC) of N points in the plane is the smalest circle that encloses these points. The problem of computing the MSC of N stochastically varying points in the plane is considered. We propose a solution to the problem that involves a heirarchy of learning automata. The automata used in this solution are the Absorbing discretized linear Inaction-Penalty (ADLIP) automata, which are the only known linear automata which are of an inaction-penalty type and yet asymptotically optimal.

18 citations


Journal ArticleDOI
TL;DR: An analog automaton is a finite state automaton where the state is defined in terms of real numbers representing physical quantities such a position, velocity, mass or color.
Abstract: Conway's Lifegame is a trivial and wellknown application of a more general theory called the theory of cellular automata. Complex systems modeling may be based on the theory of cellular automata, originated by John von Neumann. Our approach is to define simple components that we call “analog automata”. An analog automaton is a finite state automaton where the state is defined in terms of real numbers representing physical quantities such a position, velocity, mass or color. Deterministic state transition function are applied to these automata using information from the state of neighboring automata. In our case, successive generations in the evolution of these cellular automata are mapped onto polygonal meshes in order to build and texture arbitrary surfaces.

15 citations


Book ChapterDOI
01 Jan 1986
TL;DR: The marked advantage of this subclass of automata is the existence of a potential function allowing prescription of weightings on inputs to each binary device in order to choose steady state attractors with desired properties such as location in state space, and stability to perturbation.
Abstract: The past decade has seen renewed interest in non Von Neuman computation by parallel processing systems. This interest on the part of solid state physicists and others has led to models of pattern recognition and associative memory (1,2,3). In these models, it is largely the dynamical attractors which are of interest as the classes, or memories, stored in the systems. Further, the mathematical tractability of threshold systems with symmetric coupling, that is, in which each binary device “fires” if a weighted sum of excitation minus inhibition exceeds some threshold, and couplings between two binary devices are symmetrical, has focused particular attention on this subclass of automata. The marked advantage of this subclass of automata is the existence of a potential function allowing prescription of weightings on inputs to each binary device in order to choose steady state attractors with desired properties such as location in state space, and stability to perturbation (1,2,3).

15 citations


Journal ArticleDOI
TL;DR: A necessary and sufficient condition is given for a class of automata to be (homomorphically) complete for the α0-product, based on the Krohn-Rhodes Decomposition Theorem.

12 citations


Book ChapterDOI
12 May 1986

8 citations


Proceedings Article
01 Jun 1986

Journal ArticleDOI
TL;DR: This paper considers two machine models equivalent in power to Turing machines and shows their equivalence to terminal weighted regular grammars, thus proving that time varying generalized finite automata have the same power as Turing machines.
Abstract: In this paper, we consider two machine models equivalent in power to Turing machines. Time varying finite automata are defined and it is shown that time varying nondeterministic finite automata are equivalent to time varying deterministic finite automata. But, we find that, when e-moves are introduced, the power is increased to that of Turing machines. Equivalence between time varying regular grammars [6] and time varying nondeterministic finite automata with e-moves is shown. We also consider time varying generalized finite automata and show their equivalence to terminal weighted regular grammars [5], thus proving that time varying generalized finite automata have the same power as Turing machines.

Journal ArticleDOI
Chen Shihua1
TL;DR: All weakly invertible finite automata with delay τ of which M′ is a weak inverse with delay, can be constructed; and a universal nondeterministic finite automaton, for all infinite automata, is constructed.
Abstract: In this paper, we first give a method that for any inverse finite automaton M′ with delay τ, all inver tible finite automata with delay τ, of whichM′ is an inverse with delay τ, can be constructed; and a universal nondeterministic finite automaton, for all finite automata of whichM′ is an inverse with delay τ, can also be constructed. We then give a method that for any weak inverse finite automatonM′ with delay τ, all weakly invertible finite automata with delay τ of whichM′ is a weak inverse with delay, can be constructed; and a universal nondeterministic finite automaton, for all finite automata of whichM′ is a weak inverse with delay τ, can also be constructed.

01 Sep 1986
TL;DR: This paper shows how Real-Time can be introduced into the algebraic description of finite automata, to provide a tool for modelling discrete-event-systems.
Abstract: This paper shows how Real-Time can be introduced into the algebraic description of finite automata, to provide a tool for modelling discrete-event-systems

Journal ArticleDOI
TL;DR: It is shown that m log m space (m2 space) is necessary and sufficient for deterministic three-way two-dimensional Turing machines to simulate deterministic (nondeterministic) three- way two- dimensional finite automata with rotated inputs.


Journal ArticleDOI
TL;DR: This paper attempts a more detailed examination of the properties of δ-BCA (k, l), and compares its accepting power with those of other automata operating on the two-dimensional tape.
Abstract: Previously, we proposed a (k, l)-neighborhood template δ-type bounded cellular acceptor (abbreviated as δ--BCA (k, l)), which is composed of a pair of converters and a configuration-reader and operates on a two-dimensional tape. Its basic properties have already been discussed. δ-BCA (k, l) is a parallel automaton, which, in a sense, is a generalization of the one-dimensional bounded cellular acceptor. This paper attempts a more detailed examination of the properties of δ-BCA (k, l), and compares its accepting power with those of other automata operating on the two-dimensional tape. The objects of comparison are the various kinds of two-dimensional finite automata and various kinds of parallel sequential array acceptors. It is known that there exists an equivalent tape-bounded Turing machine for each of these automata in the sense of the accepting power. Consequently, the comparison of the accepting power of δ-BCA (k, l) and those of two-dimensional automata amounts in a sense to the evaluation of the accepting power of δ-BCA (k, l) in terms of the tape complexity of the tape-bounded Turing machine.


01 Jan 1986
TL;DR: The main theorem allows an elegant algorithm to be refined into an efficient one based on 'marking of' regular expressions, and works for the usual operations of union, concatenation, and iteration.
Abstract: The main theorem allows an elegant algorithm to be refined into an efficient one. The elegant algorithm for constructing a finite automaton from a regular expression is based on 'derivatives of' regular expressions; the efficient algorithm is based on 'marking of' regular expressions. Derivatives of regular expressions correspond to state transitions in finite automata. When a finite automaton makes a transition under input symbol a, a leading a is stripped from the remaining input. Correspondingly, if the input string is generated by a regular expression E, then the derivative of E by a generates the remaining input after a leading a is stripped. Brzozowski (1964) used derivatives to construct finite automata; the state for expression E has a transition under a to the state for the derivative of E by a. This approach extends to regular expressions with new operators, including intersection and complement; however, explicit computation of derivatives can be expensive. Marking of regular'expressions yields an expression with distinct input symbols. Following MeNaughton and Yamada (1960), we attach subscripts to each input symbol in an expression; (ab+b)*ba becomes (atb2+b3)*b4as. Conceptually, the efficient algorithm constructs an automaton for the marked expression. The marks on the transitions are then erased, resulting in a nondeterministic automaton for the original unmarked expression. This approach works for the usual operations of union, concatenation, and iteration; however, intersection and complement cannot be handled because marking and unmarking do not preserve the languages generated by regular expressions with these operators.

Book ChapterDOI
Uwe Quasthoff1
01 Jan 1986
TL;DR: This work describes a nesting procedure which replaces the cells by smaller and smaller ones so that one can have arbitrary small cells and arbitrary small time units while the macroscopic structure is still the same.
Abstract: Cellular automata by definition consist of discrete cells containing these automata and work in discrete time To model continuous processes, we describe a nesting procedure which replaces the cells by smaller and smaller ones so that one can have arbitrary small cells and arbitrary small time units while the macroscopic structure is still the same We investigate automata with simple neighborhood structure whether they admit such a nesting procedure or not