Rudimentary Reductions Revisited

Abstract We show that log-bounded rudimentary reductions (defined and studied by Jones in 1975) characterize Dlogtime-uniform AC 0 .

[1]  Samuel R. Buss,et al.  The Boolean formula value problem is in ALOGTIME , 1987, STOC.

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

[3]  Function Algebras,et al.  Bounded Arithmetic and Computational Complexity , 1990 .

[4]  Neil Immerman,et al.  Expressibility as a complexity measure: results and directions , 1987, SCT.

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

[6]  A. J. Wilkie,et al.  Applications of complexity theory to Σo-definability Problems in arithmetic , 1980 .

[7]  Hugo Volger.  The role of rudimentary relations in complexity theory , 1984 .

[8]  R. Smullyan.  Theory of formal systems , 1962 .

[9]  Peter Clote,et al.  Bounded arithmetic and computational complexity , 1990, Proceedings Fifth Annual Structure in Complexity Theory Conference.

[10]  Neil D. Jones.  Corrigendum: Space-Bounded Reducibility among Combinatorial Problems , 1977, J. Comput. Syst. Sci..

[11]  Arto Salomaa,et al.  Formal languages , 1973, Computer science classics.

[12]  Michael Sipser,et al.  Parity, circuits, and the polynomial-time hierarchy , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[13]  Michael Sipser,et al.  Borel sets and circuit complexity , 1983, STOC.

[14]  Neil D. Jones,et al.  Space-Bounded Reducibility among Combinatorial Problems , 1975, J. Comput. Syst. Sci..

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

[16]  J. Håstad.  Computational limitations of small-depth circuits , 1987 .

[17]  Miklós Ajtai,et al.  ∑11-Formulae on finite structures , 1983, Ann. Pure Appl. Log..

[18]  Celia Wrathall,et al.  Rudimentary Predicates and Relative Computation , 1978, SIAM J. Comput..

[19]  A. Yao.  Separating the polynomial-time hierarchy by oracles , 1985 .

[20]  Peter C. Chapin.  Formal languages I , 1973, CSC '73.

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

[22]  Samuel R. Buss,et al.  An Optimal Parallel Algorithm for Formula Evaluation , 1992, SIAM J. Comput..

[23]  Andrew Chi-Chih Yao,et al.  Separating the Polynomial-Time Hierarchy by Oracles (Preliminary Version) , 1985, FOCS.