Investigation of a model of probabilistic automata for detecting changes in the state of resources of autonomous measurement systems

An algorithmic approach based on the methods of adaptive intelligent technology for monitoring the state of objects of computer systems is considered. The approach is focused on detecting changes in the state of controlled resources of autonomous information and measurement systems: communication channel, processor, memory, and battery. An adaptive model is presented using a Bayesian classifier for estimating changes in the state of resources of autonomous information and measurement systems. The model is based on a probabilistic automaton with adaptive self-tuning. The paper describes an approach that allows increasing the duration of continuous operation of the system for monitoring environmental parameters. This approach is based on adaptive correction of primary meter readings in the event of a decrease in their accuracy due to degradation failures.

GENERAL ALGORITHMS FOR TESTING THE AMBIGUITY OF FINITE AUTOMATA AND THE DOUBLE-TAPE AMBIGUITY OF FINITE-STATE TRANSDUCERS

We present efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with ε-transitions. We give an algorithm for testing the exponential ambiguity of an automaton A in time [Formula: see text], and finite or polynomial ambiguity in time [Formula: see text], where |A|E denotes the number of transitions of A. These complexities significantly improve over the previous best complexities given for the same problem. Furthermore, the algorithms presented are simple and based on a general algorithm for the composition or intersection of automata. Additionally, we give an algorithm to determine in time [Formula: see text] the degree of polynomial ambiguity of a polynomially ambiguous automaton A and present an application of our algorithms to an approximate computation of the entropy of a probabilistic automaton. We also study the double-tape ambiguity of finite-state transducers. We show that the general problem is undecidable and that it is NP-hard for acyclic transducers. We present a specific analysis of the double-tape ambiguity of transducers with bounded delay. In particular, we give a characterization of double-tape ambiguity for synchronized transducers with zero delay that can be tested in quadratic time and give an algorithm for testing the double-tape ambiguity of transducers with bounded delay.

ON THE COMPUTATION OF THE RELATIVE ENTROPY OF PROBABILISTIC AUTOMATA

We present an exhaustive analysis of the problem of computing the relative entropy of two probabilistic automata. We show that the problem of computing the relative entropy of unambiguous probabilistic automata can be formulated as a shortest-distance problem over an appropriate semiring, give efficient exact and approximate algorithms for its computation in that case, and report the results of experiments demonstrating the practicality of our algorithms for very large weighted automata. We also prove that the computation of the relative entropy of arbitrary probabilistic automata is PSPACE-complete. The relative entropy is used in a variety of machine learning algorithms and applications to measure the discrepancy of two distributions. We examine the use of the symmetrized relative entropy in machine learning algorithms and show that, contrarily to what is suggested by a number of publications in that domain, the symmetrized relative entropy is neither positive definite symmetric nor negative definite symmetric, which limits its use and application in kernel methods. In particular, the convergence of training for learning algorithms is not guaranteed when the symmetrized relative entropy is used directly as a kernel, or as the operand of an exponential as in the case of Gaussian Kernels. Finally, we show that our algorithm for the computation of the entropy of an unambiguous probabilistic automaton can be generalized to the computation of the norm of an unambiguous probabilistic automaton by using a monoid morphism. In particular, this yields efficient algorithms for the computation of the Lp-norm of a probabilistic automaton.