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Documents authored by Valeriote, Matt

Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2020.110
Sensitive Instances of the Constraint Satisfaction Problem

Authors: Libor Barto, Marcin Kozik, Johnson Tan, and Matt Valeriote

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
We investigate the impact of modifying the constraining relations of a Constraint Satisfaction Problem (CSP) instance, with a fixed template, on the set of solutions of the instance. More precisely we investigate sensitive instances: an instance of the CSP is called sensitive, if removing any tuple from any constraining relation invalidates some solution of the instance. Equivalently, one could require that every tuple from any one of its constraints extends to a solution of the instance. Clearly, any non-trivial template has instances which are not sensitive. Therefore we follow the direction proposed (in the context of strict width) by Feder and Vardi in [Feder and Vardi, 1999] and require that only the instances produced by a local consistency checking algorithm are sensitive. In the language of the algebraic approach to the CSP we show that a finite idempotent algebra 𝔸 has a k+2 variable near unanimity term operation if and only if any instance that results from running the (k, k+1)-consistency algorithm on an instance over 𝔸² is sensitive. A version of our result, without idempotency but with the sensitivity condition holding in a variety of algebras, settles a question posed by G. Bergman about systems of projections of algebras that arise from some subalgebra of a finite product of algebras. Our results hold for infinite (albeit in the case of 𝔸 idempotent) algebras as well and exhibit a surprising similarity to the strict width k condition proposed by Feder and Vardi. Both conditions can be characterized by the existence of a near unanimity operation, but the arities of the operations differ by 1.
Cite as

Libor Barto, Marcin Kozik, Johnson Tan, and Matt Valeriote. Sensitive Instances of the Constraint Satisfaction Problem. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 110:1-110:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{barto_et_al:LIPIcs.ICALP.2020.110,
  author =	{Barto, Libor and Kozik, Marcin and Tan, Johnson and Valeriote, Matt},
  title =	{{Sensitive Instances of the Constraint Satisfaction Problem}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{110:1--110:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.110},
  URN =		{urn:nbn:de:0030-drops-125176},
  doi =		{10.4230/LIPIcs.ICALP.2020.110},
  annote =	{Keywords: Constraint satisfaction problem, bounded width, local consistency, near unanimity operation, loop lemma}
}
Document
DOI: 10.4230/DagSemProc.09441.3
On the Expression Complexity of Equivalence and Isomorphism of Primitive Positive Formulas

Authors: Matt Valeriote, Simone Bova, and Hubie Chen

Published in: Dagstuhl Seminar Proceedings, Volume 9441, The Constraint Satisfaction Problem: Complexity and Approximability (2010)

Abstract
We study the complexity of equivalence and isomorphism on primitive positive formulas with respect to a given structure. We study these problems for various fixed structures; we present generic hardness and complexity class containment results, and give classification theorems for the case of two-element (boolean) structures.
Cite as

Matt Valeriote, Simone Bova, and Hubie Chen. On the Expression Complexity of Equivalence and Isomorphism of Primitive Positive Formulas. In The Constraint Satisfaction Problem: Complexity and Approximability. Dagstuhl Seminar Proceedings, Volume 9441, pp. 1-20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{valeriote_et_al:DagSemProc.09441.3,
  author =	{Valeriote, Matt and Bova, Simone and Chen, Hubie},
  title =	{{On the Expression Complexity of Equivalence and Isomorphism of Primitive Positive Formulas}},
  booktitle =	{The Constraint Satisfaction Problem: Complexity and Approximability},
  pages =	{1--20},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9441},
  editor =	{Andrei A. Bulatov and Martin Grohe and Phokion G. Kolaitis and Andrei Krokhin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09441.3},
  URN =		{urn:nbn:de:0030-drops-23690},
  doi =		{10.4230/DagSemProc.09441.3},
  annote =	{Keywords: Expression complexity, equivalence, isomorphism, primitive positive formulas}
}
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