Graph isomorphism is low for PP

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 577 LNCS, Issue , 1992, Pages 401-411

  Köbler, Johannes ^a   Schöning, Uwe ^a   Torán, Jacobo ^b  

^a UNIVERSITY OF ULM   (Germany)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTER SCIENCE; COMPUTERS;

AUTOMORPHISMS; GRAPH AUTOMORPHISMS; GRAPH ISOMORPHISM; GRAPH ISOMORPHISM PROBLEM; GROUP FACTORIZATIONS;

SET THEORY;

EID: 85029612746     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-55210-3_200     Document Type: Conference Paper

References (39)

1. L. Babai, Moderately exponential bound for graph isomorphism. In Proceedings Fundamentals of Computation Theory, Lecture Notes in Computer Science 117 (1981), 34-50.
2. L. Babai, S. Moran, Arthur-Merlin games: A randomized proof system, and a hierarchy of complexity classes. In Journal of Computer and System Sciences 36 (1988), 254-276.
3. J.L. Balcázar, J. Díaz, J. Gabarró, Structural Complexity I. Springer, 1987.
4. R. Beigel, J. Gill, U. Hertrampf, Counting classes: Thresholds, parity, mods, and fewness. In Proceedings 7th Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science 415 (1990), 49-57.
5. NP[log] (Formula Present). In Proceedings 4th Structure in Complexity Theory Conference, p. 225-227, IEEE Computer Society, 1989.
6. R. Boppana, J. Hastad, and S. Zachos, Does co-NP have short interactive proofs? In Information Processing Letters 25 (1987), 127-132.
7. J. Cai, L.A. Hemachandra, On the power of parity. In Proceedings 6th Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science 349 (1989), 229-240.
8. S.A. Cook, The complexity of theorem-proving procedures. In Proceedings of the 3rd ACM Symposium on Theory of Computing 1971, 151-158.
9. S. Even, A. Selman Y. Yacobi, The complexity of promise problems with applications to public-key cryptography. In Information and Control 61 (1984), 114-133.
10. S. Fenner, L. Fortnow, S. Kurtz, Gap-definable counting classes. In Proceedings of the 6th Structure in Complexity Theory Conference 1991, 30-42.
11. M. Furst, J. Hopcroft, E. Luks, Polynomial time algorithms for permutation groups. In Proceedings of the 21st ACM Symposium on Theory of Computing 1980, 36-41.
12. M.R. Garey, D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, 1979.
13. J. Gill, Computational complexity of probabilistic Turing machines. In SIAM Journal on Computing 6 (1977), 675-695.
14. O. Goldreich, S. Micali, and A. Wigderson, Proofs that yield nothing but their validity and a methodology of cryptographic protocol design. In Proceedings of the 27th Symposium on Foundations of Computer Science 1986, 174-187.
15. S. Goldwasser, S. Micali, and C. Rackoff, The knowledge complexity of interactive proofs. In Proceedings of the 17th ACM Symposium on the Theory of Computing 1985, 291-304.
16. S. Goldwasser, M. Sipser, Private coins versus public coins in interactive proof systems. In Proceedings of the 18th ACM Symposium on the Theory of Computing 1986, 59-68.
17. F. Green, On the Power of Deterministic Reductions to C=P. Technical Report LSI-91-14 Universidad Politecnica de Catalunya, 1991.
18. M. Hall, The Theory of Groups, Macmillan, New York, 1959.
19. C. Hoffmann, Group-Theoretic Algorithms and Graph Isomorphism, Springer-Verlag Lecture Notes in Computer Science #136, 1982.
20. C. Hoffmann, Subcomplete generalizations of graph isomorphism. In Journal of Computer and System Sciences 25 (1982), 332-359.
21. D.S. Johnson, The NP-completeness column: An ongoing guide. In Journal of Algorithms 6 (1985), 434-451.
22. D. Kratsch, L.A. Hemachandra, On the complexity of graph reconstruction. In Fundamentals of Computing Theory 1991, to appear.
23. J. Köbler, U. Schöning, J. Torán and S. Toda, Turing Machines with few accepting computations and low sets for PP. In Proceedings of the 4th Structure in Complexity Theory Conference 1989, 208-216.
24. E. Luks, Isomorphism of Graphs of Bounded Valence can be tested in Polynomial Time. In Journal of Computer and System Sciences 25 (1982), 42-65.
25. R. Mathon, A note on the graph isomorphism counting problem. In Inform. Process. Lett. 8 (1979), 131-132.
26. M. Ogiwara, L. Hemachandra, A complexity theory for closure properties. In Proceedings of the 6th Structure in Complexity Theory Conference 1991, 16-29.
27. C. Papadimitriou, S. Zachos Two remarks on the power of counting. In 6th GI Conference on Theoretical Computer Science, Lecture Notes in Computer Science 145 (1983) 269-276.
28. U. Schöning, Complexity and Structure. Springer-Verlag Lecture Notes in Computer Science 211, 1986.
29. U. Schöning, Graph isomorphism is in the low hierarchy. In Journal of Computer and System Sciences 37 (1988), 312-323.
30. J. Simon, On some central problems in computational complexity. Ph.D. Thesis, Cornell University (1975).
31. C. Sims, Computation with permutation groups. In Proceedings of the 2nd ACM Symposium on Symbolic and Algebraic Manipulations 1971, 23-28.
32. J. Tarui, Degree complexity of boolean functions and its applications to relativized separations. In Proceedings of the 6th Structure in Complexity Theory Conference 1991, 382-390.
33. S. Toda, On the computational power of PP and ⊕P. In Proceedings of the 30th Symposium on Foundations of Computer Science 1989, 514-519.
34. S. Toda, Private communication.
35. J. Torán, An oracle characterization of the Counting Hierarchy. In Proceedings of the 3rd Structure in Complexity Theory Conference 1988, 213-224.
36. L.G. Valiant, The relative complexity of checking and evaluating. In Information Processing Letters 5 (1976), 20-23.
37. L.G. Valiant, The complexity of computing the permanent. In Theoretical Computer Science 8 (1979), 189-201.
38. L.G. Valiant, V.V Vazirani, NP is as easy as detecting unique solutions In Theoretical Computer Science 47 (1986), 85-93.
39. K.W. Wagner, The complexity of combinatorial problems with succinct input representation. In Acta Informatica 23 (1986), 325-356.