Application of artificial intelligence in the branch and bound method on the example of various applied problems

The article describes the possible approaches to the use of artificial intelligence to improve the work of the branch and bound method in various applied problems. Various developments obtained by the authors earlier in the study of the branch and bound method are used, as well as new solutions to the problems are considered

Some new heuristical algorithms for minimization of nondeterministic finite automata

In this paper, we propose an algorithm example for the transformation of so-called complete automaton given by a table of binary relation #. At the same time, we know that for this table for the binary relation #, there exists some corresponding nondeterministic automaton having Waterloo-like badness. The proposed transformation, which is not equivalent, is the serial removal of a state and combining a pair of states. It gives the opportunity to build on the basis of the given relation # some automaton which also has the walibad-property. And, generally speaking, the obtained automaton is different from the known in advance

Geometrical regular languages and linear Diophantine equations: The strongly connected case

AbstractGiven an arbitrarily large alphabet Σ, we consider the family of regular languages over Σ for which the deterministic minimal automaton has a strongly connected state diagram. We present a new method for checking whether such a language is semi-geometrical or not and whether it is geometrical or not. This method makes use of the enumeration of the simple cycles of the state diagram. It is based on the construction of systems of linear Diophantine equations, where the coefficients are deduced from the set of simple cycles

Reduction of the Nondeterministic Finite Automata

Nedeterministický konečný automat je důležitým nástrojem, který se používá pro zpracování řetězců v mnoha různých oblastech programování. V rámci zvýšení efektivity programů je důležité snažit se o zmenšování jeho velikosti. Tento problém je však velmi výpočetně náročný, proto je potřeba hledat nové postupy. V této práci jsou uvedeny základy konečných automatů a poté jsou představeny různé metody zabývající se jejich redukcí. Použitelné redukční algoritmy jsou v práci podrobněji popsány, dále implementovány a otestovány. Nakonec jsou výsledky zhodnoceny.Nondeterministic finite automaton is an important tool, which is used to process strings in many different areas of programming. It is important to try to reduce its size for increasing programs' effectiveness. However, this problem is computationally hard, so we need to search for new techniques. Basics of finite automata are described in this work. Some methods for their reduction are then introduced. Usable reduction algorithms are described in greater detail. Then they are implemented and tested. The test results are finally evaluated.

Reducing nondeterministic finite automata with SAT solvers

We consider the problem of reducing the number of states of nondeterministic finite automata, and show how to encode the reduction as a Boolean satisfiability problem. This approach improves on previous work by reducing a more general class of automata. Experimental results show that it produces a minimal automaton in almost all cases and that the running time compares favourably to the Kameda-Weiner algorithm. © 2010 Springer-Verlag Berlin Heidelberg.Conference Pape