Exact Satisfiabitity with Jokers

  • Gordon Hoi
  • Sanjay JainEmail author
  • Sibylle Schwarz
  • Frank Stephan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11436)


The XSAT problem asks for solutions of a set of clauses where for every clause exactly one literal is satisfied. The present work investigates a variant of this well-investigated topic where variables can take a joker-value (which is preserved by negation) and a clause is satisfied iff either exactly one literal is true and no literal has a joker value or exactly one literal has a joker value and no literal is true. While JX2SAT is in polynomial time, the problem becomes NP-hard when one searches for a solution with the minimum number of jokers used and the decision problem X3SAT can be reduced to the decision problem of the JX2SAT problem with a bound on the number of jokers used. JX3SAT is in both cases, with or without optimisation of the number of jokers, NP-hard and X3SAT can be reduced to it without increasing the number of variables. Furthermore, the general JXSAT problem can be solved in the same amount of time as variable-weighted XSAT and the obtained solution has the minimum amount of number of jokers possible.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Gordon Hoi
    • 1
  • Sanjay Jain
    • 1
    Email author
  • Sibylle Schwarz
    • 2
  • Frank Stephan
    • 3
  1. 1.School of ComputingNational University of SingaporeSingaporeRepublic of Singapore
  2. 2.Fakultät Informatik, Mathematik und NaturwissenschaftenHochschule für Technik, Wirtschaft und Kultur LeipzigLeipzigGermany
  3. 3.Department of Mathematics and School of ComputingNational University of SingaporeSingaporeRepublic of Singapore

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