Search results for "Automata"
showing 10 items of 453 documents
Distributed learning automata-based scheme for classification using novel pursuit scheme
2020
Learning Automata (LA) is a popular decision making mechanism to “determine the optimal action out of a set of allowable actions” (Agache and Oommen, IEEE Trans Syst Man Cybern-Part B Cybern 2002(6): 738–749, 2002). The distinguishing characteristic of automata-based learning is that the search for the optimising parameter vector is conducted in the space of probability distributions defined over the parameter space, rather than in the parameter space itself (Thathachar and Sastry, IEEE Trans Syst Man Cybern-Part B Cybern 32(6): 711–722, 2002). Recently, Goodwin and Yazidi pioneered the use of Ant Colony Optimisation (ACO) for solving classification problems (Goodwin and Yazidi 2016). In th…
On the Size Complexity of Deterministic Frequency Automata
2013
Austinat, Diekert, Hertrampf, and Petersen [2] proved that every language L that is (m,n)-recognizable by a deterministic frequency automaton such that m > n/2 can be recognized by a deterministic finite automaton as well. First, the size of deterministic frequency automata and of deterministic finite automata recognizing the same language is compared. Then approximations of a language are considered, where a language L′ is called an approximation of a language L if L′ differs from L in only a finite number of strings. We prove that if a deterministic frequency automaton has k states and (m,n)-recognizes a language L, where m > n/2, then there is a language L′ approximating L such that L′ c…
Monadic second-order logic over pictures and recognizability by tiling systems
1994
We show that a set of pictures (rectangular arrays of symbols) is recognized by a finite tiling system if and only if it is definable in existential monadic second-order logic. As a consequence, finite tiling systems constitute a notion of recognizability over two-dimensional inputs which at the same time generalizes finite-state recognizability over strings and matches a natural logic. The proof is based on the Ehrenfeucht-FraIsse technique for first-order logic and an implementation of “threshold counting” within tiling systems.
Monadic Second-Order Logic over Rectangular Pictures and Recognizability by Tiling Systems
1996
Abstract It is shown that a set of pictures (rectangular arrays of symbols) is recognized by a finite tiling system iff it is definable in existential monadic second-order logic. As a consequence, finite tiling systems constitute a notion of recognizability over two-dimensional inputs which at the same time generalizes finite-state recognizability over strings and also matches a natural logic. The proof is based on the Ehrenfeucht–Fraisse technique for first-order logic and an implementation of “threshold counting” within tiling systems.
Recent results on syntactic groups of prefix codes
2012
International audience; We give a simplified presentation of groups in transformation monoids. We use this presentation to describe two recent results on syntactic groups of prefix codes. The first one uses Sturmian words to build finite bifix codes with a given permutation group as syntactic group. The second one describes a class of prefix codes such that all their syntactic groups are cyclic.
A Generalization of Girod's Bidirectional Decoding Method to Codes with a Finite Deciphering Delay
2012
Girod’s encoding method has been introduced in order to efficiently decode from both directions messages encoded by using finite prefix codes. In the present paper, we generalize this method to finite codes with a finite deciphering delay. In particular, we show that our decoding algorithm can be realized by a deterministic finite transducer. We also investigate some properties of the underlying unlabeled graph.
Suffix Automata and Standard Sturmian Words
2007
Blumer et al. showed (cf. [3,2]) that the suffix automaton of a word w must have at least |w|+1 states and at most 2|w|-1 states. In this paper we characterize the language L of all binary words w whose minimal suffix automaton S(w) has exactly |w| + 1 states; they are precisely all prefixes of standard Sturmian words. In particular, we give an explicit construction of suffix automaton of words that are palindromic prefixes of standard words. Moreover, we establish a necessary and sufficient condition on S(w) which ensures that if w ∈ L and a ∈ {0, 1} then wa ∈ L. By using such a condition, we show how to construct the automaton S(wa) from S(w). More generally, we provide a simple construct…
Some Decision Results on Nonrepetitive Words
1985
The paper addresses some generalizations of the Thue Problem such as: given a word u, does there exist an infinite nonrepetitive overlap free (or square free) word having u as a prefix? A solution to this as well as to related problems is given for the case of overlap free words on a binary alphabet.
On Using the Theory of Regular Functions to Prove the ε-Optimality of the Continuous Pursuit Learning Automaton
2013
Published version of a chapter in the book: Recent Trends in Applied Artificial Intelligence. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-642-38577-3_27 There are various families of Learning Automata (LA) such as Fixed Structure, Variable Structure, Discretized etc. Informally, if the environment is stationary, their ε-optimality is defined as their ability to converge to the optimal action with an arbitrarily large probability, if the learning parameter is sufficiently small/large. Of these LA families, Estimator Algorithms (EAs) are certainly the fastest, and within this family, the set of Pursuit algorithms have been considered to be the pioneering schemes. The…
A Conclusive Analysis of the Finite-Time Behavior of the Discretized Pursuit Learning Automaton
2019
Author's accepted version (post-print). © 20XX IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Available from 20/03/2021. This paper deals with the finite-time analysis (FTA) of learning automata (LA), which is a topic for which very little work has been reported in the literature. This is as opposed to the asymptotic steady-state analysis for which there are, probabl…