The connection between the fundamental groupoid and a unification algorithm for syntactil algebras (extended abstract)
The cyclicity problem for the images of Q-rational series
We show that it is decidable whether or not a given Q-rational series in several noncommutative variables has a cyclic image. By definition, a series r has a cyclic image if there is a rational number q such that all nonzero coefficients of r are integer powers of q.
The cyclicity problem for the images of Q-rational series
We show that it is decidable whether or not a given Q-rational series in several noncommutative variables has a cyclic image. By definition, a series r has a cyclic image if there is a rational number q such that all nonzero coefficients of r are integer powers of q.
The decidability of the equivalence problem for polynomially bounded DOL sequences
The Diamond Tool: a way of effective development and utilization of knowledge
This paper presents the Diamond Tool for knowledge management. The main objective of its specification and implementation was to create a universal and easily extendable tool for efficient work with knowledge. One of its extensions is the eTrium technology. The principal idea behind this technology is to represent explicitly the knowledge used by the information system by means of a knowledge agent built on the Diamond Tool – in contrary to current approaches, where knowledge is present implicitly...
The difference and truth-table hierarchies for NP
The discrete logarithm problem over prime fields: the safe prime case. The Smart attack, non-canonical lifts and logarithmic derivatives
We connect the discrete logarithm problem over prime fields in the safe prime case to the logarithmic derivative.
The entropy and redundancy of normalized database structures
The entropy of Łukasiewicz-languages
The paper presents an elementary approach for the calculation of the entropy of a class of languages. This approach is based on the consideration of roots of a real polynomial and is also suitable for calculating the Bernoulli measure. The class of languages we consider here is a generalisation of the Łukasiewicz language.
The entropy of Łukasiewicz-languages
The paper presents an elementary approach for the calculation of the entropy of a class of languages. This approach is based on the consideration of roots of a real polynomial and is also suitable for calculating the Bernoulli measure. The class of languages we consider here is a generalisation of the Łukasiewicz language.
The extent to which linear problems have linear optimal algorithms
The factor automaton
This paper concerns searching substrings in a string using the factor automaton. The factor automaton is a deterministic finite automaton constructed to accept every substring of the given string. Nondeterministic factor automaton is used to achieve new operations on factor automata for searching in non-constant texts.
The family of languages satisfying Bar-Hillel's lemma
The finite automata approaches in stringology
We present an overview of four approaches of the finite automata use in stringology: deterministic finite automaton, deterministic simulation of nondeterministic finite automaton, finite automaton as a model of computation, and compositions of finite automata solutions. We also show how the finite automata can process strings build over more complex alphabet than just single symbols (degenerate symbols, strings, variables).
The first-order theory of ordering constraints over feature trees.
The Formalization of Decision-Free Petri Net
In this article we formalize the definition of Decision-Free Petri Net (DFPN) presented in [19]. Then we formalize the concept of directed path and directed circuit nets in Petri nets to prove properties of DFPN. We also present the definition of firing transitions and transition sequences with natural numbers marking that always check whether transition is enabled or not and after firing it only removes the available tokens (i.e., it does not remove from zero number of tokens). At the end of this...
The globals of pseudovarieties of ordered semigroups containing and an application to a problem proposed by Pin
Given a basis of pseudoidentities for a pseudovariety of ordered semigroups containing the 5-element aperiodic Brandt semigroup , under the natural order, it is shown that the same basis, over the most general graph over which it can be read, defines the global. This is used to show that the global of the pseudovariety of level of Straubing-Thérien’s concatenation hierarchy has infinite vertex rank.
The globals of pseudovarieties of ordered semigroups containing B2 and an application to a problem proposed by Pin
Given a basis of pseudoidentities for a pseudovariety of ordered semigroups containing the 5-element aperiodic Brandt semigroup B2, under the natural order, it is shown that the same basis, over the most general graph over which it can be read, defines the global. This is used to show that the global of the pseudovariety of level 3/2 of Straubing-Thérien's concatenation hierarchy has infinite vertex rank.
The growth functions of finitely generated semigroups.
The helping hierarchy
Schöning [14] introduced a notion of helping and suggested the study of the class of the languages that can be helped by oracles in a given class . Later, Ko [12], in order to study the connections between helping and “witness searching”, introduced the notion of self-helping for languages. We extend this notion to classes of languages and show that there exists a self-helping class that we call which contains all the self-helping classes. We introduce the Helping hierarchy whose levels are...