Victor Selivanov | Novosibirsk State University (original) (raw)

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Papers by Victor Selivanov

Lecture Notes in Computer Science, 2018

Using an extension of the notion of polynomial time presentable structure we show that some natur... more Using an extension of the notion of polynomial time presentable structure we show that some natural presentations of the ordered field \({\mathbb R}_{\text{ alg }}\) of algebraic reals and of the field \({\mathbb C}_{\text{ alg }}\) of algebraic complex numbers are polynomial-time equivalent to each other and are polynomial time. We also establish upper complexity bounds for the problem of rational polynomial evaluation in \({\mathbb C}_{\text{ alg }}\) and for the problem of root-finding for polynomials in \({\mathbb C}_{\text{ alg }}[x]\) which improve the previously known bound.

Doklady Mathematics, 2018

Lecture Notes in Computer Science, 2013

We characterize up to isomorphism the Boolean algebras of regular ω-languages and of regular aper... more We characterize up to isomorphism the Boolean algebras of regular ω-languages and of regular aperiodic ω-languages, and show decidability of classes of languages related to these characterizations.

Unveiling Dynamics and Complexity, 2017

We extend some results about Wadge degrees of Borel subsets of Baire space to finite partitions o... more We extend some results about Wadge degrees of Borel subsets of Baire space to finite partitions of Baire space. A typical new result is the characterization up to isomorphism of the Wadge degrees of k-partitions with \(\mathbf {\Delta }^0_3\)-components.

Lobachevskii Journal of Mathematics, 2020

Journal of Mathematical Sciences

Computability and continuity are closely linked – in fact, continuity can be seen as computabilit... more Computability and continuity are closely linked – in fact, continuity can be seen as computability relative to an arbitrary oracle. As such, concepts from topology and descriptive set theory feature heavily in the foundations of computable analysis. Conversely, techniques developed in computability theory can be fruitfully employed in topology and descriptive set theory, even if the desired results mention no computability at all. In this Dagstuhl Seminar, we brought together researchers from computable analysis, from classical computability theory, from descriptive set theory, formal topology, and other relevant areas. Our goals were to identify key open questions related to this interplay, to exploit synergies between the areas and to intensify collaboration between the relevant communities. Seminar November 14–19, 2021 – http://www.dagstuhl.de/21461 2012 ACM Subject Classification Theory of computation → Computability; Theory of computation → Logic; Mathematics of computing → Top...

Well-Quasi Orders in Computation, Logic, Language and Reasoning, 2020

The aim of the seminar was to discuss and systematize the recent fast progress in automata theory... more The aim of the seminar was to discuss and systematize the recent fast progress in automata theory and to identify important directions for future research. For this, the seminar brought together more than 40 researchers from automata theory and related fields of applications. We had 19 talks of 30 minutes and 5 one-hour lectures leaving ample room for discussions. In the following we describe the topics in more detail.

From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501 ``Advances and Applications of Automata... more From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501 ``Advances and Applications of Automata on Words and Trees'' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.

We investigate the effectivizations of several equivalent definitions of quasi-Polish spaces and ... more We investigate the effectivizations of several equivalent definitions of quasi-Polish spaces and study which characterizations hold effectively. Being a computable effectively open image of the Baire space is a robust notion that admits several characterizations. We show that some natural effectivizations of quasi-metric spaces are strictly stronger.

Paris-Diderot, FR, Jean-Eric.Pin@liafa.univ-paris-diderot.fr 3 A. P. Ershov Institute-Novosibirsk... more Paris-Diderot, FR, Jean-Eric.Pin@liafa.univ-paris-diderot.fr 3 A. P. Ershov Institute-Novosibirsk, RU, vseliv@iis.nsk.su 4 Universität Siegen, DE, spreen@math.uni-siegen.de Abstract Duality allows one to move between the two worlds: the world of certain algebras of properties and a spacial world of individuals, thereby leading to a change of perspective that may, and often does, lead to new insights. Dualities have given rise to active research in a number of areas of theoretical computer science. Dagstuhl Seminar 13311 "Duality in Computer Science" was held to stimulate research in this area. This report collects the ideas that were presented and discussed during the course of the seminar. Seminar License Creative Commons BY 3.0 Unported license © Mai Gehrke, Jean-Eric Pin, Victor Selivanov, and Dieter Spreen This seminar concentrated on applications of duality in computation, semantics, and formal languages. Duality and computation Consider the area of exact real number ...

A Polish space is not always homeomorphic to a computably presented Polish space. In this article... more A Polish space is not always homeomorphic to a computably presented Polish space. In this article, we examine degrees of non-computability of presenting homeomorphic copies of Polish spaces. We show that there exists a 0'-computable low_3 Polish space which is not homeomorphic to a computable one, and that, for any natural number n, there exists a Polish space X_n such that exactly the high_2n+3-degrees are required to present the homeomorphism type of X_n. We also show that no compact Polish space has an easiest presentation with respect to Turing reducibility.

From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501 "Advances and Applications of Auto... more From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501 "Advances and Applications of Automata on Words and Trees" was held in Schloss Dagstuhl-Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available. The aim of the seminar was to discuss and systematize the recent fast progress in automata theory and to identify important directions for future research. For this, the seminar brought together more than 40 researchers from automata theory and related fields of applications. We had 19 talks of 30 minutes and 5 one-hour lectures leaving ample room for discussions. In the following we give a collection ...

Abstract. We try to develop a theory of ω-regular partitions in parallel with the theory around t... more Abstract. We try to develop a theory of ω-regular partitions in parallel with the theory around the Wagner hierarchy of regular ω-languages. In particular, we generalize a theorem of L. Staiger and K. Wagner to the case of partitions, prove decidability of all levels of the Boolean hierarchy of regular partitions over open sets, establish coincidence of reducibilities by continuous functions and by functions computed by finite automata on the class of regular ∆ 0 2-partitions, and show undecidability of the firstorder theory of the structure of Wadge degrees of regular k-partitions for all k ≥ 3.

Descriptional Complexity of Formal Systems, 2021