Arithmetic complexity, Kleene closure, and formal power series

Theory of Computing Systems

Volumn 36, Issue 4, 2003, Pages 303-328

  Allender, Eric ^a   Arvind, V ^b   Mahajan, Meena ^b  

^a RUTGERS UNIVERSITY   (United States)

^b INSTITUTE OF MATHEMATICAL SCIENCES   (India)

Author keywords

[No Author keywords available]

Indexed keywords

ROOT EXTRACTION;

CONTEXT FREE LANGUAGES; INVERSE KINEMATICS; PROBLEM SOLVING; THEOREM PROVING;

COMPUTATIONAL COMPLEXITY;

EID: 0041993930     PISSN: 14324350     EISSN: 14330490     Source Type: Journal    
DOI: 10.1007/s00224-003-1077-7     Document Type: Article

References (47)

1. 0, and arithmetic circuits. Journal of Computer and System Sciences, 60:395-421, 2000.
2. [ABI] E. Allender, J. Balcázar, and N. Immerman. A first-order isomorphism theorem. SIAM Journal on Computing, 26(2):557-567, April 1997.
3. 0 circuits with negated constants. In Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science (MFCS), Lecture Notes in Computer Science 1450, pages 409-419. Springer-Verlag, Berlin, 1998.
4. [Al1] E. Allender. Making computation count: arithmetic circuits in the nineties. In L. Hemaspaandra, editor, SIGACT News Complexity Theory Column, volume 4, pages 2-15. ACM SIGACT, New York, 1997.
5. [Al2] E. Allender. The division breakthroughs. In The Computational Complexity Column in Bulletin of the EATCS, volume 74, pages 61-77. EATCS, 2001.
6. [AO] E. Allender and M. Ogihara. Relationships among PL, #L, and the determinant. RAIRO Theoretical Information and Application, 30:1-21, 1996.
7. [AR] E. Allender and K. Reinhardt. Isolation, matching, and counting. In Proceedings of the 13th Annual IEEE Conference on Computational Complexity, pages 92-100, 1998.
8. [ARZ] E. Allender, K. Reinhardt, and S. Zhou. Isolation, matching and counting: uniform and nonuniform upper bounds. Journal of Computer and System Sciences, 59:164-181, 1999.
9. 1. Journal of Computer and System Sciences, 38:150-164, 1989.
10. [Be] S. J. Berkowitz. On computing the determinant in small parallel time using a small number of processors. Information Processing Letters, 18:147-150, 1984.
11. [BLM] F. Bedard, F. Lemieux, and P. McKenzie. Extensions to Barrington's M-program model. Theoretical Computer Science, 107:31-61, 1993.
12. [BR] J. Berstel and C. Reutenauer. Rational Series and Their Languages, volume 12 of EATCS Monographs on Theoretical Computer Science. Springer-Verlag, New York, 1984.
13. 1. Journal of the Association of Computing Machinery, 35:941-952, 1988.
14. 1. RAIRO Theoretical Informatics and Applications, 35:259-276, 2001.
15. 1 computation. Journal of Computer and Systems Sciences, 57:200-212, 1998.
16. [Co] S. Cook. A taxonomy of problems with fast parallel algorithms. Information and Control, 64:2-22, 1985.
17. [FFK] S. A. Fenner, L. J. Fortnow, and S. A. Kurtz. Gap-definable counting classes. Journal of Computer and System Sciences, 48(1): 116-148, February 1994.
18. [FS] P. Flajolet and J. Steyaert. Complexity of classes of languages and operators. Technical Report Rap. de Recherche 92, IRIA Laboria, November 1974.
19. [Gi] S. Ginsburg. Algebraic and Automata-Theoretic Properties of Formal Languages. North-Holland, Amsterdam. 1975.
20. [HAB] W. Hesse, E. Allender, and D. A. M. Barrington. Uniform constant-depth threshold circuits for division and iterated multiplication. Journal of Computer and System Sciences, 65:695-716, 2002.
21. 0. In Proceedings of the International Coloquium on Automata, Languages and Programming (ICALP), pages 104-114. Lecture Notes in Computer Science 2076. Springer-Verlag, Berlin, 2001.
22. [HT1] T. M. Hoang and T. Thierauf. The complexity of the characteristic and the minimal polynomial. Theoretical Computer Science, 295(1-3):205-222, 2003.
23. [HT2] T. M. Hoang and T. Thierauf. The computational complexity of the inertia. In Proceedings of the 22nd International Conference on Foundations of Software Technology and Theoretical Computer Science (FST&TCS), pages 206-217. Lecture Notes in Computer Science, 2556. Springer-Verlag, Berlin, 2002.
24. [Im] H. Immerman. Languages which capture complexity classes. SIAM Journal on Computing, 4: 760-778, 1987.
25. [KS] W. Kuich and A. Salomaa. Semirings, Automata, Languages. EATCS Monograph. Springer-Verlag, New York, 1985.
26. [La1] K.-J. Lange. Decompositions of nondeterministic reductions. Theoretical Computer Science, 58:175-181, 1988.
27. [La2] K.-J. Lange. Complexity and structure in formal language theory. Fundamenta Informaticae, 25:327-352, 1996. Preliminary version in Proceedings of the 8th IEEE Structure in Complexity Theory Conference, pages 224-238, 1993.
28. [LH] K.-J. Lange and M. Holzer. On the complexity of iterated insertions. In G. Paun and A. Salomaa, editors, Trends in Formal Languages, Lecture Notes in Computer Science 1218, pages 440-453. Springer-Verlag, Berlin, 1997.
29. [li] L. Li. Formal power series: an algebraic approach to the GapP and #P functions. In Proceedings of the 7th Structure in Complexity Theory Conference, pages 144-154, 1992.
30. [Mo] B. Monien. About the deterministic simulation of nondeterministic (log n)-tape bounded Turing machines. In Proceedings of the 2nd GI Conference, Lecture Notes in Computer Science 33, pages 118-126. Springer-Verlag, Berlin, 1975.
31. 1: the automata-theoretic viewpoint. Computational Complexity, 1:330-359, 1991.
32. [MV] M. Mahajan and V. Vinay. Determinant: combinatorics, algorithms, and complexity. Chicago Journal of Theoretical Computer Science, volume 1997, article 5, 1997. Preliminary version in Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 730-738, 1997.
33. [Pi] J. E. Pin. Varieties of Formal Languages. North Oxford Academic, London, 1986.
34. [RA] K. Reinhardt and E. Allender. Making nondeterminism unambiguous. SIAM Journal on Computing, 29:1118-1131, 2000. Preliminary version in Proceedings of the 38th IEEE Conference on Foundations of Computer Science, pages 244-253, 1997.
35. [Sa] A. Salomaa. Formal languages and power series. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, Volume B, pages 103-132. Elsevier, Amsterdam, 1990.
36. [Sc] M. P. Schützenberger. On finite monoids having only trivial subgroups. Information and Control, 8:190-194, 1965.
37. [SS] A. Salomaa and M. Soittola. Automata-Theoretic Aspects of Formal Power Series. Springer-Verlag, New York. 1978.
38. [St1] I. A. Stewart. Methods for proving completeness via logical reductions. Theoretical Computer Science, 118(2): 193-229, September 1993.
39. [St2] I.A. Stewart. Completeness of path-problems via logical reductions. Information and Computation, 121(1):123-134, August 1995.
40. [To1] S. Toda. Counting problems computationally equivalent to the determinant. Manuscript, 1991.
41. [To2] S. Toda. Classes of arithmetic circuits capturing the complexity of computing the determinant. IEICE Transactions on Information and Systems, E75-D:116-124, 1992.
42. [Ve1] H. Venkateswaran. Properties that characterize LogCFL. Journal of Computer and System Sciences, 42:380-404, 1991.
43. [Ve2] H. Venkateswaran. Circuit definitions of nondeterministic complexity classes. SIAM Journal on Computing, 21:655-670, 1992.
44. [Vi1] V. Vinay. Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits. In Proceedings of the 6th Structure in Complexity Theory Conference, pages 270-284, 1991.
45. [Vi2] V. Vinay. Semi-unboundedness and complexity classes. Ph.D. thesis, Indian Institute of Science, Bangalore, 1991.
46. [Vo] H. Vollmer. Introduction to Circuit Complexity: A Uniform Approach. Springer-Verlag, New York, 1999.
47. [Wa] J. Watrous. On quantum and classical space-bounded processes with algebraic transition amplitudes. In Proceedings of the 40th IEEE Symposium on Foundations of Computer Science, pages 341-351, 1999.