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## On Computational Complexity of Set Automata

P. 332-344.

Rubtsov A. A., Vyalyi M.

We consider a computational model which is known as set automata. The set automata are one-way finite automata with an additional storage---the set. There are two kinds of set automata---the deterministic and the nondeterministic ones. We denote them as DSA and NSA respectively. The model was introduced by M. Kutrib, A. Malcher, M. Wendlandt in 2014 in [3, 4]. It was shown that DSA-languages look similar to DCFL due to their closure properties and NSA-languages look similar to CFL due to their undecidability properties.

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Cham : Springer, 2017

Rubtsov A. A., Vyalyi M., , in : Descriptional Complexity of Formal Systems. Vol. 9118.: Switzerland : Springer, 2015. P. 256-267.

We investigate regular realizability (RR) problems, which are the prob- lems of verifying whether intersection of a regular language – the input of the problem – and fixed language called filter is non-empty. In this pa- per we focus on the case of context-free filters. Algorithmic complexity of the RR problem is a very coarse ...

Added: August 25, 2015

Rubtsov A. A., Vyalyi M., , in : Computer Science – Theory and Applications 13th International Computer Science Symposium in Russia, CSR 2018, Moscow, Russia, June 6–10, 2018, Proceedings. Vol. 10846.: Springer, 2018. P. 295-307.

We consider a computational model which is known as set automata.
The set automata are one-way finite automata with an additional storage—the set. There are two kinds of set automata—the deterministic and the nondeterministic ones. We denote them as DSA and NSA respectively. The model was introduced by Kutrib et al. in 2014 in [2, 3].
In this ...

Added: June 21, 2018

Vyalyi M., Rubtsov A. A., Проблемы передачи информации 2015 Т. 51 № 4 С. 47-59

We consider regular realizability problems, which consist in verifying whether the intersection of a regular language which is the problem input and a fixed language (filter) which is a parameter of the problem is nonempty. We study the algorithmic complexity of regular realizability problems for context-free filters. This characteristic is consistent with the rational dominance ...

Added: February 14, 2016

[б.и.], 2016

Added: September 18, 2017

Springer, 2020

Added: October 22, 2018

Rubtsov A. A., Vyalyi M., Information and Computation 2021 Vol. 281 Article 104797

We consider a computational model which is known as set automata. The set automata are one-way finite automata with additional storage-the set. There are two kinds of set automata-deterministic (DSA's) and nondeterministic (NSA's). The model was introduced by Kutrib, Malcher, Wendlandt in 2014. It was shown that DSA-recognizable languages look similar to DCFL's and NSA-recognizable ...

Added: February 2, 2022

Konev B. Y., Lutz C., Wolter F. et al., , in : 25th International Joint Conference on Artificial Intelligence. : [б.и.], 2016. P. 1153-1159.

We investigate the problem of conservative rewritability of a TBox T in a description logic (DL) L into a TBox T' in a weaker DL L'. We focus on model-conservative rewritability (T' entails T and all models of T are expandable to models of T'), subsumption-conservative rewritability (T' entails T and all subsumptions in the ...

Added: September 18, 2017

Rubtsov A. A., Vyalyi M., Information and Computation 2019

We consider a computational model which is known as set automata. The set automata are one-way finite automata with an additional storage— the set. There are two kinds of set automata—the deterministic and the nondeterministic ones. We denote them as DSA and NSA respectively. The model was introduced by M. Kutrib, A. Malcher, M. Wendlandt ...

Added: October 22, 2018

Cham : Springer, 2017

The 21st International Conference on Developments in Language Theory (DLT 2017) was organized by the Department of Mathematics of the University of Liège, Belgium, during August 7–11, 2017.
The DLT conference series is one of the major international conference series in language theory and related areas. The DLT conference was established by G. Rozenberg and A. ...

Added: September 5, 2017

Rubtsov Alexander, , in : Abstracts of Reports and other materials of the 7th School "Computer Science Days in Ekaterinburg". : Ekaterinburg : Ural Fedearal University, 2014. P. 25-27.

Added: October 17, 2014

Rybakov M., Shkatov D., Journal of Logic and Computation 2021 Vol. 31 No. 2 P. 426-443

It is shown that products and expanding relativized products of propositional modal logics where one component is the minimal monomodal logic K are polynomial-time reducible to their single-variable fragments. Therefore, the nown lower bound complexity and undecidability results for such logics are extended to their single-variable fragments. Similar results are obtained for products where one component is a polymodal logic with a K-style ...

Added: September 24, 2020

Yaroslav Shitov, Linear Algebra and its Applications 2013 Vol. 439 No. 8 P. 2500-2502

We present a reduction which shows that the fooling set number, tropical and determinantal ranks of a Boolean matrix are NP-hard to compute. ...

Added: August 11, 2013

American Association for Artificial Intelligence (AAAI) Press, 2015

Added: September 18, 2017

Malyshev D., Дискретная математика 2009 Т. 21 № 4 С. 129-134

The notion of a boundary class is a useful notion in the investigation of the complexity of extremal problems on graphs. One boundary class is known for the independent set problem and three boundary classes are known for the dominating set problem. In this paper it is proved that the set of boundary classes for ...

Added: November 25, 2012

Aleskerov F. T., Meshcheryakova N., Shvydun S. et al., , in : 6th International Conference on Computers Communications and Control (ICCCC) 2016. : Oradea : Agora University, 2016. P. 118-123.

The problem of quick detection of central nodes in large networks is studied. There are many measures that allow to evaluate a topological importance of nodes of the network. Unfortunately, most of them cannot be applied to large networks due to their high computational complexity. However, if we narrow the initial network and apply these ...

Added: June 8, 2016

Korpelainen N., Lozin V. V., Malyshev D. et al., Theoretical Computer Science 2011 No. 412 P. 3545-3554

The notion of a boundary graph property was recently introduced as a relaxation of that of a minimal property and was applied to several problems of both algorithmic and combinatorial nature. In the present paper, we first survey recent results related to this notion and then apply it to two algorithmic graph problems: Hamiltonian cycle ...

Added: September 11, 2012

Sirotkin D., Журнал Средневолжского математического общества 2018 Т. 20 № 2 С. 199-205

The vertex 3-colourability problem is to determine for a given graph whether one can divide its vertex set into three subsets of pairwise non-adjacent vertices. This problem is NP-complete in the class of planar graphs, but it becomes polynomial-time solvable for planar triangulations, i.e. planar graphs, all facets of which (including external) are triangles. Additionally, ...

Added: July 2, 2018

Sirotkin D., Malyshev D., Journal of Applied and Industrial Mathematics 2018 Vol. 12 No. 4 P. 759-769

The 3-coloring problem for a given graph consists in verifying whether it is possible
to divide the vertex set of the graph into three subsets of pairwise nonadjacent vertices. A complete
complexity classification is known for this problem for the hereditary classes defined by triples of
forbidden induced subgraphs, each on at most 5 vertices. In this article, ...

Added: November 20, 2018

Malyshev D., Дискретный анализ и исследование операций 2012 Т. 19 № 6 С. 37-48

Понятие граничного класса графов является полезным инструментом для анализа вычислительной сложности задач на графах в семействе наследственных классов. В предыдущих работах автора исследовались общие черты и особенности семейств граничных классов графов для задачи о вершинной k-раскраске и ее «предельного варианта» - задачи о хроматическом числе. В данной работе эта проблематика рассматривается применительно к реберному варианту ...

Added: November 30, 2012

Malyshev D., Journal of Applied and Industrial Mathematics 2013 Vol. 7 No. 2 P. 221-228

The notion of a boundary class of graphs is a helpful tool for the computational complexity analysis of graph theory problems in the family of hereditary classes. Some general and specific features for families of boundary classes of graphs for the vertex k-colorability problem and its “limit” variant, the chromatic index problem, were studied by ...

Added: June 23, 2013

Alekseev V., Lozin V. V., Malyshev D. et al., Lecture Notes in Computer Science 2008 Vol. 5162 No. 4 P. 96-107

We study the computational complexity of finding a maximum independent set of vertices in a planar graph. In general, this problem is known to be NP-hard. However, under certain restrictions it becomes polynomial-time solvable. We identify a graph parameter to which the complexity of the problem is sensible and produce a number of both negative ...

Added: November 7, 2012

Malyshev D., Discrete Mathematics and Applications 2010 Vol. 19 No. 6 P. 625-630

The notion of a boundary class is a useful notion in the investigation of the complexity of extremal problems on graphs. One boundary class is known for the independent set problem and three boundary classes are known for the dominating set problem. In this paper it is proved that the set of boundary classes for ...

Added: November 25, 2012

Malyshev D., Journal of Applied and Industrial Mathematics 2012 Vol. 6 No. 1 P. 97-99

Under study is the complexity status of the independent set problem in a class of connected graphs that are defined by functional constraints on the number of edges depending on the number of vertices. For every natural number C, this problem is shown to be polynomially solvable in the class of graphs, On the other ...

Added: December 7, 2012