Limits of Symmetric Computation (Invited Talk)

Author Anuj Dawar



PDF
Thumbnail PDF

File

LIPIcs.ICALP.2024.1.pdf
  • Filesize: 0.52 MB
  • 8 pages

Document Identifiers

Author Details

Anuj Dawar
  • Department of Computer Science and Technology, University of Cambridge, UK

Cite AsGet BibTex

Anuj Dawar. Limits of Symmetric Computation (Invited Talk). In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 1:1-1:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ICALP.2024.1

Abstract

I survey recent work on symmetric computation. A number of strands of work, from logic, circuit complexity, combinatorial optimization and other areas have converged on similar notions of symmetry in computation. This write-up of an invited talk gives a whirlwind tour through the results and pointers to the relevant literature.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity theory and logic
  • Theory of computation → Finite Model Theory
  • Theory of computation → Complexity classes
Keywords
  • Logic
  • Complexity Theory
  • Symmetric Computation

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. S. Abramsky, A. Dawar, and P. Wang. The pebbling comonad in finite model theory. In 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017, 2017. URL: https://doi.org/10.1109/LICS.2017.8005129.
  2. M. Anderson and A. Dawar. On symmetric circuits and fixed-point logics. Theory Comput. Syst., 60(3):521-551, 2017. URL: https://doi.org/10.1007/s00224-016-9692-2.
  3. M. Anderson, A. Dawar, and B. Holm. Solving linear programs without breaking abstractions. J. ACM, 62, 2015. Google Scholar
  4. A. Atserias, A. Bulatov, and A. Dawar. Affine systems of equations and counting infinitary logic. Theoretical Computer Science, 410(18):1666-1683, 2009. Google Scholar
  5. A. Atserias, A. Dawar, and J. Ochremiak. On the power of symmetric linear programs. J. ACM, 68:26:1-26:35, 2021. URL: https://doi.org/10.1145/3456297.
  6. A. Atserias and J. Fijalkow. Definable ellipsoid method, sums-of-squares proofs, and the graph isomorphism problem. SIAM J. Comput., 52:1193-1229, 2023. URL: https://doi.org/10.1137/20M1338435.
  7. L. Barto and M. Kozik. Constraint satisfaction problems solvable by local consistency methods. J. ACM, 61:3:1-3:19, 2014. Google Scholar
  8. A. A. Bulatov. A dichotomy theorem for nonuniform csps. In 58th IEEE Annual Symposium on Foundations of Computer Science, FOCS, pages 319-330, 2017. URL: https://doi.org/10.1109/FOCS.2017.37.
  9. A. A. Bulatov, P. Jeavons, and A. A. Krokhin. Classifying the complexity of constraints using finite algebras. SIAM J. Comput., 34(3):720-742, 2005. Google Scholar
  10. J-Y. Cai, M. Fürer, and N. Immerman. An optimal lower bound on the number of variables for graph identification. Combinatorica, 12(4):389-410, 1992. Google Scholar
  11. A. Dawar. The nature and power of fixed-point logic with counting. ACM SIGLOG News, 2(1):8-21, 2015. Google Scholar
  12. A. Dawar, E. Grädel, B. Holm, E. Kopczynski, and W. Pakusa. Definability of linear equation systems over groups and rings. Logical Methods in Computer Science, 9, 2013. URL: https://doi.org/10.2168/LMCS-9(4:12)2013.
  13. A. Dawar, E. Grädel, and W. Pakusa. Approximations of isomorphism and logics with linear-algebraic operators. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019), volume 132 of Leibniz International Proceedings in Informatics (LIPIcs), pages 112:1-112:14, 2019. URL: https://doi.org/10.4230/LIPIcs.ICALP.2019.112.
  14. A. Dawar, M. Grohe, B. Holm, and B. Laubner. Logics with rank operators. In 2009 24th Annual IEEE Symposium on Logic In Computer Science, pages 113-122. IEEE, 2009. Google Scholar
  15. A. Dawar, E. Grädel, and M. Lichter. Limitations of the invertible-map equivalences. Journal of Logic and Computation, 33:961-969, 2023. URL: https://doi.org/10.1093/logcom/exac058.
  16. A. Dawar and B. Holm. Pebble games with algebraic rules. Fundam. Informaticae, 150:281-316, 2017. URL: https://doi.org/10.3233/FI-2017-1471.
  17. A. Dawar and K. Khan. Constructing hard examples for graph isomorphism. J. Graph Algorithms Appl., 23:293-316, 2019. URL: https://doi.org/10.7155/JGAA.00492.
  18. A. Dawar and P. Wang. A definability dichotomy for finite valued CSPs. In 24th EACSL Annual Conference on Computer Science Logic, CSL 2015, pages 60-77, 2015. Google Scholar
  19. A. Dawar and P. Wang. Definability of semidefinite programming and Lasserre lower bounds for CSPs. In 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS, 2017. URL: https://doi.org/10.1109/LICS.2017.8005108.
  20. A. Dawar and G. Wilsenach. Symmetric Arithmetic Circuits. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020), volume 168 of Leibniz International Proceedings in Informatics (LIPIcs), pages 36:1-36:18, 2020. URL: https://doi.org/10.4230/LIPIcs.ICALP.2020.36.
  21. A. Dawar and G. Wilsenach. Symmetric circuits for rank logic. ACM Transactions on Computational Logic (TOCL), 23:1-35, 2021. Google Scholar
  22. A. Dawar and G. Wilsenach. Lower bounds for symmetric circuits for the determinant. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022), volume 215 of Leibniz International Proceedings in Informatics (LIPIcs), pages 52:1-52:22, 2022. URL: https://doi.org/10.4230/LIPIcs.ITCS.2022.52.
  23. L. Denenberg, Y. Gurevich, and S. Shelah. Definability by constant-depth polynomial-size circuits. Information and Control, 70:216-240, 1986. Google Scholar
  24. S. A. Fenner, L.ance Fortnow, and W. I. Gasarch. Complexity theory newsflash. SIGACT News, 27:126, 1996. URL: https://doi.org/10.1145/235666.571629.
  25. E. Grädel and W. Pakusa. Rank logic is dead, long live rank logic! The Journal of Symbolic Logic, 84, March 2019. Google Scholar
  26. M. Grohe. Descriptive Complexity, Canonisation, and Definable Graph Structure Theory. Lecture Notes in Logic. Cambridge University Press, 2017. Google Scholar
  27. N. Immerman. Relational queries computable in polynomial time. Information and Control, 68:86-104, 1986. Google Scholar
  28. M. Lichter. Separating rank logic from polynomial time. J. ACM, pages 14:1-14:53, 2023. Google Scholar
  29. M. Otto. The logic of explicitly presentation-invariant circuits. In Computer Science Logic, 10th International Workshop, CSL '96, Annual Conference of the EACSL, pages 369-384, 1996. Google Scholar
  30. T. Rothvoß. The matching polytope has exponential extension complexity. In Symp. Theory of Computing, STOC 2014, pages 263-272, 2014. Google Scholar
  31. V. Vianu. Databases and finite-model theory. In N. Immerman and Ph. G. Kolaitis, editors, Descriptive Complexity and Finite Models, volume 31 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pages 97-148. AMS, 1996. URL: https://doi.org/10.1090/DIMACS/031/04.
  32. M. Yannakakis. Expressing combinatorial optimization problems by linear programs. J. Comput. Syst. Sci., 43(3):441-466, 1991. Google Scholar
  33. D. Zhuk. A proof of the CSP dichotomy conjecture. Journal of the ACM, 67:1-78, 2020. Google Scholar