Полиномиальный алгоритм проверки эквивалентности детерминированных двухленточных автоматов
It is shown how the verification of the equivalence of two-tape deterministic automata can be reduced to the problem of checking the equivalence of weakly nondeterministic finite automata-transformers working on the semigroup of prefix regular languages with the concatenation operation.
Finite state transducers over semigroups can be regarded as a formal model of sequential reactive programs. In this paper we introduce a uniform tech- nique for checking eectively functionality, k-valuedness, equivalence and inclusion for this model of computation in the case when a semigroup these transducers op- erate over is embeddable in a decidable group.
The textbook contains necessary information about universal and classical algebras, systems of axioms for the basic algebraic structures (groupoid, monoid, semi-groups, groups, partial orders, rings, fields). The basic cryptographic algorithms are described. Error-correcting codes - linear, cyclic, BCH are considered. Algorithms for designing of such codes are given. Many examples are shown. It is put in a basis of the book long-term experience of teaching by authors the discipline «Discrete mathematics» at the business informatics faculty, at the computer science faculty of National research university Higher school of economics, and at the automatics and computer technique faculty of National research university Moscow power engineering institute. The book is intended for the students of a bachelor degree, trained at the computer science faculties in the directions 09.03.01 Informatics and computational technique, 09.03.02 Informational systems and technologies, 09.03.03 Applied informatics, 09.03.04 Software Engineering, and also for IT experts and developers of software products.
We present an efficient equivalence-checking algorithm for a propositional model of programs with semantics based on (what we call) progressive monoids on the finite set of statements generated by relations of a specific form. We consider arbitrary set of relations for commutativity (relations of the form ab=ba for statements a, b) and left absorption (relations of the form ab=b for statements a, b) properties. The main results are a polynomial-time decidability for the equivalence problem in the considered case, and an explicit description of an equivalence-checking algorithm which terminates in time polynomial in size of programs.