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Games for query inseparability of description logic knowledge bases
P. 78–119.
Zakharyaschev M., Kontchakov R.
We consider conjunctive query inseparability of description logic knowledge bases with respect to a given signature - a fundamental problem in knowledge base versioning, module extraction, forgetting and knowledge exchange. We give a uniform game-theoretic characterisation of knowledge base conjunctive query inseparability and develop worst-case optimal decision algorithms for fragments of Horn-ALCHI, including the description logics underpinning OWL 2 QL and OWL 2 EL. We also determine the data and combined complexity of deciding query inseparability. While query inseparability for all of these logics is P-complete for data complexity, the combined complexity ranges from P- to ExpTime- to 2ExpTime-completeness. We use these results to resolve two major open problems for OWL 2 QL by showing that TBox query inseparability and the membership problem for universal conjunctive query solutions in knowledge exchange are both ExpTime-complete for combined complexity. Finally, we introduce a more flexible notion of inseparability which compares answers to conjunctive queries in a given signature over a given set of individuals. In this case, checking query inseparability becomes NP-complete for data complexity, but the ExpTime- and 2ExpTime-completeness combined complexity results are preserved.
Kirill V. Kaymakov, Dmitry S. Malyshev, Optimization Letters 2024 Vol. 18 P. 1273–1283
For given edge-capacitated connected graph and two its vertices s and t, the bottleneck (or max min ) path problem is to find the maximum value of path-minimum edge capacities among all paths, connecting s and t. It can be generalized by finding the bottleneck values between s and all possible t. These problems arise ...
Added: April 18, 2024
Malyshev D., Duginov O. I., Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2023 Vol. 17 No. 4 P. 791–801
For a given graph, the edge-coloring problem is to minimize the number of colors sufficient to color all the graph edges so that any adjacent edges receive different colors. For all classes defined by sets of forbidden subgraphs, each with 7 edges, the complexity status of this problem is known. In this paper, we obtain ...
Added: February 16, 2024
Gerasimova O., Makarov I., Severin N., IEEE Access 2023 Vol. 11 P. 88074–88086
The problem of query answering over incomplete attributed graph data is a challenging field of database management systems and artificial intelligence. When there are rules on data structure expressed in the form of the ontology, the theoretical complexity of finding exact solution satisfying ontology constraints increases. Logic-based methods use theoretical constructions to obtain efficient rewritings ...
Added: January 5, 2024
Sergei Valentinovich Fedorenko, IEEE Access 2023 Vol. 11 P. 62771–62779
The novel methods for binary discrete Fourier transform (DFT) computation over the finite field have been proposed. The methods are based on a binary trace calculation over the finite field and use the cyclotomic DFT. The direct DFT computational complexity has been reduced due to using the binary trace function over the finite field and ...
Added: July 19, 2023
Complexity function and complexity of validity of modal and superintuitionistic propositional logics
Rybakov M., Shkatov D., Journal of Logic and Computation 2023 Vol. 33 No. 7 P. 1566–1595
We consider the relationship between the algorithmic properties of the validity problem for a modal or superintuitionistic propositional logic and the size of the smallest Kripke countermodels for non-theorems of the logic. We establish the existence, for every degree of unsolvability, of a propositional logic whose validity problem belongs to the degree and whose every ...
Added: January 6, 2023
Malyshev D., Duginov O. I., Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2022 Vol. 16 P. 276–291
The edge-coloring problem is to minimize the number of colors sufficient to color all the edges of a given graph so that any adjacent edges receive distinct colors. The complexity status of this problem is known for all the classes defined by the sets of forbidden subgraphs with 7 edges each. In this paper, we ...
Added: December 31, 2022
G. S. Dakhno, D. S. Malyshev, Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2023 Vol. 17 No. 1 P. 25–31
A hereditary class is a set of simple graphs closed under deletion of vertices; every such class is defined by the set of its minimal forbidden induced subgraphs. If this set is finite, then the class is said to be finitely defined. The concept of a boundary class is a useful tool for the analysis ...
Added: December 6, 2022
Kochergin V., Moscow University Mathematics Bulletin 2022 Vol. 77 No. 3 P. 113–119
Abstract: The computational complexity of the element (Formula presented.) of the Abelian group (Formula presented.) (it is supposed that kii for all i) and the computational complexity of the term (Formula presented.) are compared in the paper. The computational complexity means the minimal possible number of multiplication operations, and all the results of intermediate multiplications ...
Added: October 29, 2022
Gerasimova O., Kikot S., Podolskii V. V. et al., Artificial Intelligence 2022 Vol. 309 Article 103738
Our concern is the problem of efficiently determining the data complexity of answering queries mediated by description logic ontologies and constructing their optimal rewritings to standard database queries. Originated in ontology-based data access and datalog optimisation, this problem is known to be computationally very complex in general, with no explicit syntactic characterisations available. In this ...
Added: May 30, 2022
Rybakov M., Shkatov D., Theoretical Computer Science 2022 Vol. 925 P. 45–60
We prove that branching-time temporal logics CTL and CTL* are polynomial-time embeddable into their single-variable fragments. It follows that satisfiability for CTL and CTL*, and therefore also for alternating-time temporal logics ATL and ATL*, in languages with one propositional variable is as algorithmically hard as satisfiability for the full logic: EXPTIME-complete for CTL and ATL, and 2EXPTIME-complete for CTL* and ATL*. We discuss applicability of the technique used in the proofs to other ...
Added: May 12, 2022
Malyshev D. S., Приставченко О. В., Optimization Letters 2022 Vol. 16 P. 1403–1409
The vertex 3-colourability problem is to decide whether the vertex set of a given graph
can be split into three subsets of pairwise non-adjacent vertices. This problem is known
to be NP-complete in a certain class of graphs, defined by an explicit description of
allowed 5-vertex induced subgraphs in them. In the present paper, we improve this
result by ...
Added: February 25, 2022
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
Zakharyaschev M., Savateev Y., Ryzhikov V., Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2021.
Our concern is the problem of determining the data complexity of answering an ontology-mediated query (OMQ) given in linear temporal logic LTL over (Z, <) and deciding whether it is rewritable to an FO(<)-query, possibly with extra predicates. First, we observe that, in line with the circuit complexity and FO-definability of regular languages, OMQ answering ...
Added: November 6, 2021
Zakharyaschev M., Kontchakov R., Ryzhikov V. et al., The International Joint Conference on Artificial Intelligence (IJCAI), 2020.
Traditionally, description logic has focused on represent- ing and reasoning about classes rather than relations (roles), which has been justified by the deterioration of the computa- tional properties if expressive role inclusions are added. The situation is even worse in the temporalised setting, where monodicity is viewed as an almost necessary condition for decidability. We ...
Added: November 6, 2021
Zhuk D., , in: 2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS).: [б.и.], 2021. P. 1–7.
The Surjective Constraint Satisfaction Problem (SCSP) is the problem of deciding whether there exists a surjective assignment to a set of variables subject to some specified constraints, where a surjective assignment is an assignment containing all elements of the domain. In this paper we show that the most famous SCSP, called No-Rainbow Problem, is NP-Hard. ...
Added: September 8, 2021
Barto L., Brady Z., Bulatov M. et al., , in: 2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS).: [б.и.], 2021. P. 1–13.
This paper focuses on the algebraic theory underlying the study of the complexity and the algorithms for the Constraint Satisfaction Problem (CSP). We unify, simplify, and extend parts of the three approaches that have been developed to study the CSP over finite templates - absorption theory that was used to characterize CSPs solvable by local ...
Added: September 8, 2021
Sirotkin D., Malyshev D., Lobachevskii Journal of Mathematics 2021 Vol. 42 No. 4 P. 760–766
The vertex 3-colourability problem is to verify whether it is possible to split the vertex set of a given graph into three subsets of pairwise nonadjacent vertices or not. This problem is known to be NP-complete for planar graphs of the maximum face length at most 4 (and, even, additionally, of the maximum vertex degree ...
Added: June 5, 2021
Razvenskaya O., Malyshev D., Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2021 Vol. 15 No. 1 P. 97–117
The weighted vertex coloring problem for a given weighted graph is to minimize the number of colors so that for each vertex the number of the colors that are assigned to this vertex is equal to its weight and the assigned sets of vertices are disjoint for any adjacent vertices. For all but four hereditary ...
Added: April 23, 2021
Sergei Valentinovich Fedorenko, IEEE Access 2021 Vol. 9 P. 38673–38686
A novel method for finding roots of polynomials over finite fields has been proposed.
This method is based on the cyclotomic discrete Fourier transform algorithm.
The improvement is achieved by using the normalized cyclic convolutions,
which have a small complexity and allow matrix decomposition,
as well as methods of adapting the truncated normalized cyclic convolutions calculation.
For small values of ...
Added: April 15, 2021
Malyshev D., Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2020 Vol. 14 No. 4 P. 706–721
The edge coloring problem for a graph is to minimize the number of colors that are sufficient to color all edges of the graph so that all adjacent edges receive distinct colors. The computational complexity of the problem is known for all graph classes defined by forbidden subgraphs with at most 6 edges. We improve ...
Added: January 30, 2021
Malyshev D., Optimization Letters 2021 Vol. 15 No. 2 P. 311–326
The vertex colourability problem is to determine, for a given graph and a given natural k, whether it is possible to split the graph’s vertex set into at most k subsets, each of pairwise non-adjacent vertices, or not. A hereditary class is a set of simple graphs, closed under deletion of vertices. Any such a class can be ...
Added: January 6, 2021
Gillis N., Shitov Y., Linear Algebra and its Applications 2019 Vol. 581 P. 367–382
The low-rank matrix approximation problem with respect to the entry-wise l∞-norm is the following: given a matrix M and a factorization rank r, find a matrix X whose rank is at most r and that minimizes max_i,j | M_ij − X_ij |. In this paper, we prove that the decision variant of this problem for ...
Added: November 11, 2020
Gribanov D., Malyshev D., Mokeev D. B., Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2020 Vol. 14 P. 480–489
We consider the problem of minimizing the number of colors in the colorings of the vertices of a given graph so that, to each vertex there is assigned some set of colors whose number is equal to the given weight of the vertex; and adjacent vertices receive disjoint sets. For all hereditary classes defined by ...
Added: October 30, 2020
Zhuk D., , in: 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS).: IEEE, 2017. P. 331–342.
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The standard way to parametrize interesting subclasses of the constraint satisfaction problem is via finite constraint languages. The main problem is ...
Added: October 29, 2020