The Complexity of Disjunctive Linear Diophantine Constraints

Authors Manuel Bodirsky, Barnaby Martin, Marcello Mamino, Antoine Mottet

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Manuel Bodirsky
  • Institut für Algebra, TU Dresden, Germany
Barnaby Martin
  • Department of Computer Science, Durham University, U.K.
Marcello Mamino
  • Dipartimento di Matematica, largo Pontecorvo 5, 56127 Pisa, Italy
Antoine Mottet
  • Institut für Algebra, TU Dresden, Germany

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Manuel Bodirsky, Barnaby Martin, Marcello Mamino, and Antoine Mottet. The Complexity of Disjunctive Linear Diophantine Constraints. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 33:1-33:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We study the Constraint Satisfaction Problem CSP( A), where A is first-order definable in (Z;+,1) and contains +. We prove such problems are either in P or NP-complete.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity theory and logic
  • Constraint Satisfaction
  • Presburger Arithmetic
  • Computational Complexity


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