论文信息 - The Recursion-Theoretic Structure of Complexity Classes

The Recursion-Theoretic Structure of Complexity Classes

Abstract We prove easy recursion-theoretic results which have as corollaries generalizations of existing diagonalization theorems on complexity classes: roughly speaking, almost no ‘reasonable’ (time, space or even abstract) complexity class can be expressed as the (non-trivial) union of two recursively presentable classes which are closed under finite variations (e.g. unless NP = P, NP ≠ P ∪ {NP-complete languages}); and, consequently, the non-trivial complement of one complexity class in another (e.g. (NPP), provided NP ≠ P) is almost never recursively presentable.

Diana Schmidt

[1] PAUL CHEW,et al. A Note on Structure and Looking Back Applied to the Complexity of Computable Functions , 1981, J. Comput. Syst. Sci..

[2] R.E. Ladner,et al. A Comparison of Polynomial Time Reducibilities , 1975, Theor. Comput. Sci..

[3] Richard Edwin Stearns,et al. Hierarchies of memory limited computations , 1965, SWCT.

[4] Uwe Schöning. A Uniform Approach to Obtain Diagonal Sets in Complexity Classes , 1982, Theor. Comput. Sci..

[5] Richard E. Ladner,et al. Space Bounds for Processing Contentless Inputs , 1975, J. Comput. Syst. Sci..

[6] Diana Schmidt. On the complement of one complexity class in another , 1983, Logic and Machines.

[7] Walter S. Brainerd,et al. Theory of computation , 1974 .

[8] Richard Edwin Stearns,et al. Memory bounds for recognition of context-free and context-sensitive languages , 1965, SWCT.

[9] Jeffrey D. Ullman,et al. Some Results on Tape-Bounded Turing Machines , 1969, JACM.

[10] Timothy J. Long. Strong Nondeterministic Polynomial-Time Reducibilities , 1982, Theor. Comput. Sci..

[11] Richard E. Ladner,et al. On the Structure of Polynomial Time Reducibility , 1975, JACM.

[12] Richard J. Lipton,et al. On the Structure of Sets in NP and Other Complexity Classes , 1981, Theor. Comput. Sci..

[13] Seth Breidbart. On Splitting Recursive Sets , 1978, J. Comput. Syst. Sci..

[14] Kenneth W. Regan. On Diagonalization Methods and the Structure of Language Classes , 1983, FCT.