Pavel Semukhin

In this paper we consider uncountable classes recognizable by @w-automata and investigate suitable learning paradigms for them. Expand

We give new examples of FA presentable torsion-free abelian groups and monoids using the notion of amalgamated product. Expand

The main result of this paper is the decidability of the membership problem for 2 × 2 nonsingular integer matrices. Expand

We study the relationship between computability-theoretic properties and algebraic properties of computably enumerable linearly ordered sets realized by E. Expand

We study the learnability of automatic families by automatic learners which, in each round, output a hypothesis and update a long term memory, depending on the input datum, via an automatic function, that is, via a function whose graph is recognised by a finite automaton. Expand

This paper solves two open problems about the decidability of the vector reachability problem over a finitely generated semigroup of matrices from SL(2, Z) and the point to point reachability (over rational numbers) for fractional linear transformations, where associated matrices are from SL. Expand

Automatic classes are classes of languages for which a finite automaton can decide the membership problem for the languages in the class, in a uniform way, given an index for the language. Expand

We build an א1-categorical but not א0- categorical theory whose only computably presentable model is the saturated one. Expand

We consider the membership problem for matrix semigroups and prove that this problem is decidable for 2X2 integer matrices whose determinants are equal to 0, 1, -1. Expand