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Uncountable automatic classes and learning
TLDR
In this paper we consider uncountable classes recognizable by @w-automata and investigate suitable learning paradigms for them. Expand
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Finite Automata Presentable Abelian Groups
TLDR
We give new examples of FA presentable torsion-free abelian groups and monoids using the notion of amalgamated product. Expand
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Decidability of the Membership Problem for 2 × 2 integer matrices
TLDR
The main result of this paper is the decidability of the membership problem for 2 × 2 nonsingular integer matrices. Expand
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Linear Orders Realized by C.E. Equivalence Relations
TLDR
We study the relationship between computability-theoretic properties and algebraic properties of computably enumerable linearly ordered sets realized by E. Expand
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Automatic Learners with Feedback Queries
TLDR
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
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Vector Reachability Problem in SL(2, Z)
TLDR
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
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Automatic learning of subclasses of pattern languages
TLDR
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
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Finite automata presentable abelian groups
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An Uncountably Categorical Theory Whose Only Computably Presentable Model Is Saturated
TLDR
We build an א1-categorical but not א0- categorical theory whose only computably presentable model is the saturated one. Expand
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Membership Problem in GL(2, Z) Extended by Singular Matrices
TLDR
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
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