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Dichotomy theorem for the generalized unique satisfiability problem

  • Laurent Juban
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1684)

Abstract

The unique satisfiability problem, that asks whether there exists a unique solution to a given propositional formula, was extensively studied in the recent years. This paper presents a dichotomy theorem for the unique satisfiability problem, partitioning the instances of the problem between the polynomial-time solvable and coNP-hard cases. We notice that the additional knowledge of a model makes this problem coNP-complete.We compare the polynomial cases of unique satisfiability to the polynomial cases of the usual satisfiability problem and show that they are incomparable. This difference between the polynomial cases is partially due to the necessity to apply parsimonious reductions among the unique satisfiability problems to preserve the number of solutions. In particular, we notice that the unique not-all-equal satisfiability problem, where we ask whether there is a unique model such that each clause has at least one true literal and one false literal, is solvable in polynomial time.

Keywords

Polynomial Time Dichotomy Theorem Logical Relation Conjunctive Normal Form Truth Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Laurent Juban
    • 1
  1. 1.LORIA (Universitè Henri Poincarè Nancy 1)Vandœuvre-lèes-NancyFrance

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