论文信息 - Relating the provable collapse of P to NC1 and the power of logical theories

Relating the provable collapse of P to NC1 and the power of logical theories

We show that the following three statements are equivalent: QPV is conservative over QALV, QALV proves its open induction formulas, and QALV proves P = NC 1. Here QPV and QALV are rst order theories whose function symbols range over polynomial-time and NC 1 functions, respectively.

Stephen Cook | S. Cook

[1] Samuel R. Buss,et al. Are there Hard Examples for Frege Systems , 1995 .

[2] Jan Krajícek,et al. Bounded Arithmetic and the Polynomial Hierarchy , 1991, Ann. Pure Appl. Log..

[3] François Pitt,et al. A quantifier-free theory based on a string algebra for NC1 , 1996, Proof Complexity and Feasible Arithmetics.

[4] J. Kraj,et al. On Frege and Extended Frege Proof Systems , 1993 .

[5] 外史竹内. Bounded Arithmetic と計算量の根本問題 , 1996 .

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

[7] Domenico Zambella. Notes on Polynomially Bounded Arithmetic , 1996, J. Symb. Log..

[8] Samuel R. Buss,et al. Propositional Consistency Proofs , 1991, Ann. Pure Appl. Log..

[9] David A. Mix Barrington,et al. Bounded-width polynomial-size branching programs recognize exactly those languages in NC1 , 1986, STOC '86.

[10] Samuel R. Buss. Relating the Bounded Arithmetic and Polynomial Time Hierarchies , 1995, Ann. Pure Appl. Log..

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

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

[13] Jan Krajícek,et al. Bounded arithmetic, propositional logic, and complexity theory , 1995, Encyclopedia of mathematics and its applications.