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Generic Expression Hardness Results for Primitive Positive Formula Comparison

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Automata, Languages and Programming (ICALP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6756))

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Abstract

We study the expression complexity of two basic problems involving the comparison of primitive positive formulas: equivalence and containment. We give two generic hardness results for the studied problems, and discuss evidence that they are optimal and yield, for each of the problems, a complexity trichotomy.

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References

  1. Atserias, A.: Conjunctive Query Evaluation by Search-Tree Revisited. Theoretical Computer Science 371(3), 155–168 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. Barto, L.: CD implies NU (2010) (manuscript)

    Google Scholar 

  3. Barto, L., Kozik, M.: Constraint satisfaction problems of bounded width. In: Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2009, pp. 595–603 (2009)

    Google Scholar 

  4. Berman, J., Idziak, P., Marković, P., McKenzie, R., Valeriote, M., Willard, R.: Varieties with Few Subalgebras of Powers. Transactions of the American Mathematical Society 362(3), 1445–1473 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bodnarchuk, V., Kaluzhnin, L., Kotov, V., Romov, B.: Galois Theory for Post Algebras. I, II. Cybernetics 5, 243–252, 531–539 (1969)

    Article  MATH  Google Scholar 

  6. Bova, S., Chen, H., Valeriote, M.: On the Expression Complexity of Equivalence and Isomorphism of Primitive Positive Formulas. Theory of Computing Systems,, doi:10.1007/s00224-010-9302-7

    Google Scholar 

  7. Bulatov, A., Jeavons, P., Krokhin, A.: Classifying the Complexity of Constraints using Finite Algebras. SIAM Journal on Computing 34(3), 720–742 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bulatov, A.: Tractable Conservative Constraint Satisfaction Problems. In: Proceedings of 18th IEEE Symposium on Logic in Computer Science (LICS 2003), pp. 321–330 (2003)

    Google Scholar 

  9. Bulatov, A.: A Dichotomy Theorem for Constraint Satisfaction Problems on a 3-element Set. Journal of the ACM 53 (2006)

    Google Scholar 

  10. Bulatov, A., Valeriote, M.: Recent Results on the Algebraic Approach to the CSP. In: Creignou, N., Kolaitis, P.G., Vollmer, H. (eds.) Complexity of Constraints. LNCS, vol. 5250, pp. 68–92. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  11. Freese, R., McKenzie, R.: Commutator Theory for Congruence Modular Varieties. London Mathematical Society Lecture Note Series, vol. 125. Cambridge University Press, Cambridge (1987)

    MATH  Google Scholar 

  12. Geiger, D.: Closed Systems of Functions and Predicates. Pacific Journal of Mathematics 27, 95–100 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  13. Hobby, D., McKenzie, R.: The Structure of Finite Algebras. Contemporary Mathematics, vol. 76. American Mathematical Society, Providence (1988); Revised edition: 1996

    MATH  Google Scholar 

  14. Idziak, P., Markovic, P., McKenzie, R., Valeriote, M., Willard, R.: Tractability and Learnability Arising from Algebras with Few Subpowers. In: Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science, LICS (2007)

    Google Scholar 

  15. Hunt III, H.B., Rosenkrantz, D.J., Bloniarz, P.A.: On the Computational Complexity of Algebra on Lattices. SIAM Journal on Computing 16(1), 129–148 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  16. Kearnes, K., Kiss, E., Valeriote, M.: Minimal Sets and Varieties. Transactions of the American Mathematical Society 350(1), 1–41 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  17. Kolaitis, P., Vardi, M.: Conjunctive-Query Containment and Constraint Satisfaction. Journal of Computer and System Sciences 61, 302–332 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  18. Papadimitriou, C., Yannakakis, M.: On the Complexity of Database Queries. Journal of Computer and System Sciences 58(3), 407–427 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  19. Vardi, M.: The Complexity of Relational Query Languages. In: Proceedings of the 18th Annual ACM Symposium on Theory of Computing, STOC (1982)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Vanderbilt University, Nashville, USA

    Simone Bova

  2. Departament de Tecnologies de la Informació i les Comunicacions, Universitat Pompeu Fabra, Barcelona, Spain

    Hubie Chen

  3. Department of Mathematics & Statistics, McMaster University, Hamilton, Canada

    Matthew Valeriote

Authors
  1. Simone Bova
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  2. Hubie Chen
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  3. Matthew Valeriote
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Editor information

Editors and Affiliations

  1. ICE-TCS, School of Computer Science, Reykjavik University, Menntavegur 1, IS 101, Reykjavik, Iceland

    Luca Aceto

  2. Fakultät für Informatik, Universität Wien, Universitätsstraße10/9, 1090, Wien, Österreich, Austria

    Monika Henzinger

  3. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Praha 1, Czech Republic

    Jiří Sgall

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© 2011 Springer-Verlag Berlin Heidelberg

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Bova, S., Chen, H., Valeriote, M. (2011). Generic Expression Hardness Results for Primitive Positive Formula Comparison. In: Aceto, L., Henzinger, M., Sgall, J. (eds) Automata, Languages and Programming. ICALP 2011. Lecture Notes in Computer Science, vol 6756. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22012-8_27

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  • DOI: https://doi.org/10.1007/978-3-642-22012-8_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22011-1

  • Online ISBN: 978-3-642-22012-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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