A complexity theory based on Boolean algebra

A projection of a Boolean function is a function obtained by substituting for each of its variables a variable, the negation of a variable, or a constant. Reducibilities among computational problems under this relation of projection are considered. It is shown that much of what is of everyday relevance in Turing-machine-based complexity theory can be replicated easily and naturally in this elementary framework. Finer distinctions about the computational relationships among natural problems can be made than in previous formulations and some negative results are proved.

[1]  Journal of the Association for Computing Machinery , 1961, Nature.

[2]  Walter J. Savitch,et al.  Relationships Between Nondeterministic and Deterministic Tape Complexities , 1970, J. Comput. Syst. Sci..

[3]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[4]  Sheila A. Greibach,et al.  The Hardest Context-Free Language , 1973, SIAM J. Comput..

[5]  Neil D. Jones,et al.  Complete problems for deterministic polynomial time , 1974, STOC '74.

[6]  L. Csanky,et al.  Fast parallel matrix inversion algorithms , 1975, 16th Annual Symposium on Foundations of Computer Science (sfcs 1975).

[7]  Leslie G. Valiant,et al.  Universal circuits (Preliminary Report) , 1976, STOC '76.

[8]  Leslie G. Valiant,et al.  Circuit Size is Nonlinear in Depth , 1976, Theor. Comput. Sci..

[9]  Allan Borodin,et al.  On Relating Time and Space to Size and Depth , 1977, SIAM J. Comput..

[10]  Ivan Hal Sudborough.  Time and Tape Bounded Auxiliary Pushdown Automata , 1977, MFCS.

[11]  Jacob T. Schwartz.  Probabilistic algorithms for verification of polynomial identities (invited) , 1979, EUROSAM.

[12]  Richard J. Lipton,et al.  Linear Programming is Log-Space Hard for P , 1979, Inf. Process. Lett..

[13]  L. G. H. Cijan.  A polynomial algorithm in linear programming , 1979 .

[14]  László Lovász,et al.  On determinants, matchings, and random algorithms , 1979, FCT.

[15]  Leslie G. Valiant,et al.  Completeness classes in algebra , 1979, STOC.

[16]  Stephen A. Cook,et al.  Deterministic CFL's are accepted simultaneously in polynomial time and log squared space , 1979, STOC.

[17]  Walter L. Ruzzo,et al.  Tree-size bounded alternation(Extended Abstract) , 1979, J. Comput. Syst. Sci..

[18]  Jacob T. Schwartz,et al.  Fast Probabilistic Algorithms for Verification of Polynomial Identities , 1980, J. ACM.

[19]  Joseph JáJá,et al.  Parallel Algorithms in Graph Theory: Planarity Testing (preliminary version) , 1980, MFCS.

[20]  L. Khachiyan.  Polynomial algorithms in linear programming , 1980 .

[21]  Leslie G. Valiant,et al.  Fast Parallel Computation of Polynomials Using Few Processes , 1981, MFCS.

[22]  Joseph JáJá,et al.  Parallel Algorithms in Graph Theory: Planarity Testing , 1982, SIAM J. Comput..

[23]  Leslie G. Valiant,et al.  Fast Parallel Computation of Polynomials Using Few Processors , 1983, SIAM J. Comput..