论文信息 - ALOGTIME and a conjecture of S.A. Cook

ALOGTIME and a conjecture of S.A. Cook

Using sequential, machine-independent characterizations of the parallel complexity classes AC/sup k/ and NC/sup k/, the author establishes a conjecture of S.A. Cook (1975) regarding polynomial size Frege proofs for a certain infinite family. A related result is established with constant formula-depth polynomial size Frege proofs for a system AV related to uniform AC/sup 0/ functions.<<ETX>>

Peter Clote

[1] Stephen A. Cook,et al. Functional interpretations of feasibly constructive arithmetic , 1989, STOC '89.

[2] Stephen A. Cook,et al. Feasibly constructive proofs and the propositional calculus (Preliminary Version) , 1975, STOC.

[3] Neil Immerman,et al. On Uniformity within NC¹ , 1990, J. Comput. Syst. Sci..

[4] Samuel R. Buss. Polynomial Size Proofs of the Propositional Pigeonhole Principle , 1987, J. Symb. Log..

[5] Miklós Ajtai,et al. The complexity of the Pigeonhole Principle , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[6] Neil Immerman,et al. Expressibility and Parallel Complexity , 1989, SIAM J. Comput..

[7] Stephen A. Cook,et al. The Relative Efficiency of Propositional Proof Systems , 1979, Journal of Symbolic Logic.

[8] N. Immerman,et al. On uniformity within NC 1 . , 1988 .

[9] Walter L. Ruzzo. On Uniform Circuit Complexity , 1981, J. Comput. Syst. Sci..

[10] Jan Krajícek,et al. Propositional proof systems, the consistency of first order theories and the complexity of computations , 1989, Journal of Symbolic Logic.

[11] Stephen A. Cook,et al. A Taxonomy of Problems with Fast Parallel Algorithms , 1985, Inf. Control..

[12] M. Dowd,et al. Propositional representation of arithmetic proofs , 1979 .