Showing papers in "Cybernetics and Systems Analysis in 1998"

Principles of logic optimization for a moore microprogrammed automaton

Abstract: The existence of pseudoequivalent states permits minimizing the length of the direct structural table of the Moore automaton and thus reduces the number of terms in the system of automaton memory excitation functions. Automaton logic optimization requires unique identification of the classes of pseudoequivalent states. Method M1 identifies the classesB i ∈ πga without using additional variables and states. However, the application of this method does not always reduce the DST to the corresponding parameter of the equivalent Mealy automaton. Moreover, forR > R 0 the number of feedback parameters in the Moore automaton is greater than in the equivalent Mealy automaton. Method M2 attains the absolute minimum DST length and the absolute minimum number of feedback variables, which are equal to the corresponding parameters of the equivalent Mealy automaton. Moreover, state encoding can be applied that minimizes the number of terms in the microoperation system. However, M2 requires the introduction of a special code converter and thus involves additional hardware costs.

Construction of convex continuations for functions defined on a hypersphere

Abstract: Construction of convex continuations for functions defined on the vertices of some combinatorial polyhedra, in particular the permutation polyhedron and the arrangement polyhedron, has been studied in [1, 2]. Subsequently this result has been generalized to functions defined at the extreme points of an arbitrary polyhedron [3]. For purposes of combinatorial optimization [4-6] it is relevant to consider the existence and construction of convex continuations from continua, in particular, when the function is defined on a hypersphere in thek-dimensional space. Unfortunately, passage to the limit from discrete sets to continua does not produce positive results in this case. We are thus forced to develop special approaches to investigating the existence of convex continuations of functions defined on continua.

Synthesis of continuous-valued logic functions defined in tabular form

Abstract: The choice table provides one of the techniques for the representation of functions in continuous-valued logic [1]. The need to synthesize functions from choice tables arise in the design of hybrid [2] and analog [3] computers, and also in other applications of continuous-valued logic that are surveyed in [4]. The structure of the original table is determined by the external specification of the device or unit being designed. Algorithms are available for the synthesis of continuous-valued logic functions from choice tables of a special form, for instance, from ordered choice tables [ It is noted in [ that a general algorithm to synthesize a continuous-valued logic function from an arbitrary choice table is still unknown. In the present article, we derive a criterion that decides whether a given choice table defmes some continuous-valued logic function and construct a simple algorithm to synthesize the function from the table.

Iterative methods to compute weighted normal pseudosolutions with positive definite weights

Abstract: We construct iterative processes to compute the weighted normal pseudosolution with positive definite weights (weighted least squares solutions with weighted minimum Euclidean norm) for systems of linear algebraic equations (SLAE) with an arbitrary rectangular real matrix. We examine two iterative processes based on the expansion of the weighted pseudoinversc matrix into matrix power series. The iterative processes are applied to solve constrained least squares problems that arise in mathematical programming and to findL-pseudosolutions.

Mixed method for solving the general convex programming problem

Abstract: Let us return to the claim that we made at the beginning: given the existing level of computers, computational mathematics must not ignore new opportunities for finding results that have been impossible until very recently. In our view, the proposed mixed method is consistent with technological progress: all known problems have been solved in acceptable time, and not in a single case has the method failed to produce a solution.

Separable resolution method for checking the satisfiability of formulas in the languageL

Abstract: This paper offers an effective resolution method for checking the satisfiability of a collection of disjuncts in the languageL. The method permits one to substantially reduce the number of generated resolvents in comparison with the method ofR-resolution. One more factor ensuring the efficiency of the method is a significant reduction in the number of disjunct pairs checked for the possibility of resolving them. As for the number of generated disjuncts, its greatest reduction is obtained in the case of the use of the disjunct-set partition corresponding to the limiting system of predicate-symbol subsets given by symbol ordering. It is possible to interpret the result obtained for this case as proof of the completeness of the strategy combining an ordering of predicate symbols andR-resolution. It is necessary to note that to different orderings of predicate symbols correspond different partitions of the disjunct set giving, in turn, different numbers of generated disjuncts in the process ofSp-completion. Nevertheless, the methods described in Sec. 2, which use partition of the disjunct set into two classes, are of independent importance. As has already been said, completion of a disjunct set is used for solution of a number of problems during the design of a procedural automaton specification. For example, in the case of checking the consistency of two interacting automata [5] based on completion of a disjunct set, there exists a natural partition of the predicate symbols into input and output symbols, to which corresponds the partition of the disjunct set into subsets specifying the interacting automata.

Parallel algorithm to find maximum capacity paths

Abstract: An important advantage of the proposed algorithm compared with previous algorithms is that it easily finds the maximum flow between a given pair of network nodess, t. This requires onlym repetitions of the algorithm, wherem is the number of edges in the graphG defining the given network. The time complexity of finding the maximum flow by the proposed algorithm thus does not exceed O(mn). The procedure to find the maximum flow consists of two steps.

Optimal linear extrapolation algorithm for realization of a vector random sequence observed without errors

Abstract: A number of linear extrapolation algorithms for scalar random sequences have been proposed in [1-3]. However, as a rule, the state of real technical systems is characterized by more than one independent parameter. This leads to the vector optimal extrapolation problem considered in this article. The complexity of the problem is largely determined by the fact that, in general, we cannot make any simplifying assumptions about the vector sequence being investigated. As a rule, this is a nonstationary, nonmonotone, non-Markovian, and non-Gaussian sequence generated by a nonlinear system. It is in this highly general framework that we solve our problem.

Optimization methods for compound poisson risk processes

Abstract: In this article we introduce the notion of the family of compound Poisson risk processes that depend on a finite-dimensional parameter; we describe examples of such families that arise during formalization of surplus, quota, and quota-surplus reinsurance contracts; the optimization problem is stated for the growth rate of insurance company capital subject to a given constraint on the probability of ruin; numerical methods for solving this problem by Lagrange function saddle-point techniques are reviewed.