Search results for "AUTOMATA"
showing 10 items of 453 documents
Vertical representation of C∞-words
2015
We present a new framework for dealing with C ∞ -words, based on their left and right frontiers. This allows us to give a compact representation of them, and to describe the set of C ∞ -words through an infinite directed acyclic graph G. This graph is defined by a map acting on the frontiers of C ∞ -words. We show that this map can be defined recursively and with no explicit reference to C ∞ -words. We then show that some important conjectures on C ∞ -words follow from analogous statements on the structure of the graph G.
A challenging family of automata for classical minimization algorithms
2010
In this paper a particular family of deterministic automata that was built to reach the worst case complexity of Hopcroft's state minimization algorithm is considered. This family is also challenging for the two other classical minimization algorithms: it achieves the worst case for Moore's algorithm, as a consequence of a result by Berstel et al., and is of at least quadratic complexity for Brzozowski's solution, which is our main contribution. It therefore constitutes an interesting family, which can be useful to measure the efficiency of implementations of well-known or new minimization algorithms.
A Stochastic Search on the Line-Based Solution to Discretized Estimation
2012
Published version of a chapter in the book: Advanced Research in Applied Artificial Intelligence. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-642-31087-4_77 Recently, Oommen and Rueda [11] presented a strategy by which the parameters of a binomial/multinomial distribution can be estimated when the underlying distribution is nonstationary. The method has been referred to as the Stochastic Learning Weak Estimator (SLWE), and is based on the principles of continuous stochastic Learning Automata (LA). In this paper, we consider a new family of stochastic discretized weak estimators pertinent to tracking time-varying binomial distributions. As opposed to the SLWE, our p…
On Using a Hierarchy of Twofold Resource Allocation Automata to Solve Stochastic Nonlinear Resource Allocation Problems
2007
Recent trends in AI attempt to solve difficult NP-hard problems using intelligent techniques so as to obtain approximately-optimal solutions. In this paper, we consider a family of such problems which fall under the general umbrella of "knapsack-like" problems, and demonstrate how we can solve all of them fast and accurately using a hierarchy of Learning Automata (LA). In a multitude of real-world situations, resources must be allocated based on incomplete and noisy information, which often renders traditional resource allocation techniques ineffective. This paper addresses one such class of problems, namely, Stochastic Non-linear Fractional Knapsack Problems. We first present a completely …
Achieving Fair Load Balancing by Invoking a Learning Automata-Based Two-Time-Scale Separation Paradigm.
2020
Author's accepted manuscript. © 2020 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. In this article, we consider the problem of load balancing (LB), but, unlike the approaches that have been proposed earlier, we attempt to resolve the problem in a fair manner (or rather, it would probably be more appropriate to describe it as an ε-fair manner because, although the LB…
The design of absorbing Bayesian pursuit algorithms and the formal analyses of their ε-optimality
2016
The fundamental phenomenon that has been used to enhance the convergence speed of learning automata (LA) is that of incorporating the running maximum likelihood (ML) estimates of the action reward probabilities into the probability updating rules for selecting the actions. The frontiers of this field have been recently expanded by replacing the ML estimates with their corresponding Bayesian counterparts that incorporate the properties of the conjugate priors. These constitute the Bayesian pursuit algorithm (BPA), and the discretized Bayesian pursuit algorithm. Although these algorithms have been designed and efficiently implemented, and are, arguably, the fastest and most accurate LA report…
Learning Automata-Based Solutions to Stochastic Nonlinear Resource Allocation Problems
2009
“Computational Intelligence” is an extremely wide-ranging and all-encompassing area. However, it is fair to say that the strength of a system that possesses “Computational Intelligence” can be quantified by its ability to solve problems that are intrinsically hard. One such class of NP-Hard problems concerns the so-called family of Knapsack Problems, and in this Chapter, we shall explain how a sub-field of Artificial Intelligence, namely that which involves “Learning Automata”, can be used to produce fast and accurate solutions to “difficult” and randomized versions of the Knapsack problem (KP).
A novel technique for stochastic root-finding: Enhancing the search with adaptive d-ary search
2017
The most fundamental problem encountered in the field of stochastic optimization, is the Stochastic Root Finding (SRF) problem where the task is to locate an unknown point x∗ for which g(x∗) = 0 for a given function g that can only be observed in the presence of noise [15]. The vast majority of the state-of-the-art solutions to the SRF problem involve the theory of stochastic approximation. The premise of the latter family of algorithms is to oper ate by means of so-called “small-step”processesthat explorethe search space in a conservative manner. Using this paradigm, the point investigated at any time instant is in the proximity of the point investigated at the previous time instant, render…
The Power of the “Pursuit” Learning Paradigm in the Partitioning of Data
2019
Traditional Learning Automata (LA) work with the understanding that the actions are chosen purely based on the “state” in which the machine is. This modus operandus completely ignores any estimation of the Random Environment’s (RE’s) (specified as \(\mathbb {E}\)) reward/penalty probabilities. To take these into consideration, Estimator/Pursuit LA utilize “cheap” estimates of the Environment’s reward probabilities to make them converge by an order of magnitude faster. This concept is quite simply the following: Inexpensive estimates of the reward probabilities can be used to rank the actions. Thereafter, when the action probability vector has to be updated, it is done not on the basis of th…
The Reconstruction of Polyominoes from Approximately Orthogonal Projections
2001
The reconstruction of discrete two-dimensional pictures from their projection is one of the central problems in the areas of medical diagnostics, computer-aided tomography, pattern recognition, image processing, and data compression. In this note, we determine the computational complexity of the problem of reconstruction of polyominoes from their approximately orthogonal projections. We will prove that it is NP-complete if we reconstruct polyominoes, horizontal convex polyominoes and vertical convex polyominoes. Moreover we will give the polynomial algorithm for the reconstruction of hv-convex polyominoes that has time complexity O(m3n3).