Complexity of Constraint Satisfaction Problems over Finite Subsets of Natural Numbers

Author Titus Dose

Thumbnail PDF


  • Filesize: 493 kB
  • 13 pages

Document Identifiers

Author Details

Titus Dose

Cite AsGet BibTex

Titus Dose. Complexity of Constraint Satisfaction Problems over Finite Subsets of Natural Numbers. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 32:1-32:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


We study the computational complexity of constraint satisfaction problems that are based on integer expressions and algebraic circuits. On input of a finite set of variables and a finite set of constraints the question is whether the variables can be mapped onto finite subsets of N (resp., finite intervals over N) such that all constraints are satisfied. According to the operations allowed in the constraints, the complexity varies over a wide range of complexity classes such as L, P, NP, PSPACE, NEXP, and even Sigma_1, the class of c.e. languages.
  • computational complexity
  • constraint satisfaction problems
  • integer expressions and circuits


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. E. Böhler, C. Glaßer, B. Schwarz, and K. W. Wagner. Generation problems. Theor. Comput. Sci., 345(2-3):260-295, 2005. Google Scholar
  2. M. Davis, H. Putnam, and J. Robinson. The decision problem for exponential Diophantine equations. Annals of Mathematics, 74(2):425-436, 1961. Google Scholar
  3. T. Dose. Complexity of constraint satisfaction problems over finite subsets of natural numbers. Technical Report 16-031, Electronic Colloquium on Computational Complexity (ECCC), 2016. Google Scholar
  4. T. Feder and M. Y. Vardi. The computational structure of monotone monadic snp and constraint satisfaction: A study through datalog and group theory. SIAM J. Comput., 28(1):57-104, February 1999. Google Scholar
  5. Christian Glaßer, Katrin Herr, Christian Reitwießner, Stephen D. Travers, and Matthias Waldherr. Equivalence problems for circuits over sets of natural numbers. Theory Comput. Syst., 46(1):80-103, 2010. Google Scholar
  6. C. Glaßer, B. Martin, and P. Jonsson. Circuit satisfiability and constraint satisfaction problems around skolem arithmetic. In Proceedings of the 12th International Conference on Computability in Europe (CiE-2016), Lecture Notes in Computer Science. Springer Verlag, 2016. To appear. Google Scholar
  7. C. Glaßer, C. Reitwießner, S. Travers, and M. Waldherr. Satisfiability of algebraic circuits over sets of natural numbers. Discrete Applied Mathematics, 158(13):1394 - 1403, 2010. Google Scholar
  8. R. Greenlaw, H. J. Hoover, and W. L. Ruzzo. A Compendium of Problems Complete for P, 1991. Google Scholar
  9. D. E. Knuth. All questions answered. Notices of the AMS, 49(3):318-324, 2002. Google Scholar
  10. Y. V. Matiyasevich. Enumerable sets are Diophantine. Doklady Akad. Nauk SSSR, 191:279-282, 1970. Translation in Soviet Math. Doklady, 11:354-357, 1970. Google Scholar
  11. Pierre McKenzie and Klaus W. Wagner. The complexity of membership problems for circuits over sets of natural numbers. Computational Complexity, 16(3):211-244, 2007. Google Scholar
  12. C. M. Papadimitriou. Computational complexity. Addison-Wesley, Reading, Massachusetts, 1994. Google Scholar
  13. Omer Reingold. Undirected connectivity in log-space. J. ACM, 55(4):17:1-17:24, September 2008. Google Scholar
  14. L. J. Stockmeyer and A. R. Meyer. Word problems requiring exponential time: Preliminary report. In Proceedings of the Fifth Annual ACM Symposium on Theory of Computing, STOC '73, pages 1-9, New York, NY, USA, 1973. ACM. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail