Efficient Enumeration of Solutions Produced by Closure Operations

Authors Arnaud Mary, Yann Strozecki

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Arnaud Mary
Yann Strozecki

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Arnaud Mary and Yann Strozecki. Efficient Enumeration of Solutions Produced by Closure Operations. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 52:1-52:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


In this paper we address the problem of generating all elements obtained by the saturation of an initial set by some operations. More precisely, we prove that we can generate the closure by polymorphisms of a boolean relation with a polynomial delay. Therefore we can compute with polynomial delay the closure of a family of sets by any set of "set operations" (e.g. by union, intersection, difference, symmetric difference ...). To do so, we prove that for any set of operations F, one can decide in polynomial time whether an element belongs to the closure by F of a family of sets. When the relation is over a domain larger than two elements, we prove that our generic enumeration method fails, since the associated decision problem is NP-hard.
  • enumeration
  • set saturation
  • polynomial delay
  • Post’s lattice


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