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Abstract: This paper shows that classical results about complexity classes involving "delayed diagonalization" and "gap languages," such as Ladner's Theorem and Schoning's Theorem and independence results of a kind noted by Schoning and Hartmanis, apply at very low levels of complexity, indeed all the way down in Sipser's log-time hierarchy. This paper also investigates refinements of Sipser's classes and notions of log-time reductions, following on from recent work by Cai, Chen, and others. 1... (Update)
Context of citations to this paper: More
...restrictive resource bounds are sucient for performing Ladner style delayed diagonalization constructions. Remark 55. Regan and Vollmer [28] show results on partial order embeddings for various reducibilities of many one type that run in logarithmic time. Typically, for given...
.... with Generalized Acceptance Criteria 181 proviso U) model which does not delete its index tape after a read operation, see [CC95, RV97] This means that, even with a logarithmic time bound, such a machine may access logarithmically many bits of its input; this fact allows...
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BibTeX entry: (Update)
K. Regan and H. Vollmer. Gap-languages and log-time complexity classes. Theoretical Computer Science, 188:101--116, 1997. http://citeseer.ist.psu.edu/71335.html More
@article{ regan97gaplanguages,
author = "Kenneth W. Regan and Heribert Vollmer",
title = "Gap-languages and log-time complexity classes",
journal = "Theoretical Computer Science",
volume = "188",
number = "1--2",
pages = "101--116",
year = "1997",
url = "citeseer.ist.psu.edu/71335.html" }
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141 The complexity of finite functions (context) - Boppana, Sipser - 1990
125 On uniform circuit complexity (context) - Ruzzo - 1981
103 Almost optimal lower bounds for small-depth circuits - Hastad - 1989
94 the structure of polynomial-time reducibility (context) - Ladner - 1975
82 Hierarchical memory with block transfer (context) - Aggarwal, Chandra et al. - 1987
70 The boolean formula value problem is in ALOGTIME - Buss - 1987
60 On uniformity within NC (context) - Barrington, Immerman et al. - 1990
48 A complexity theory based on Boolean algebra (context) - Skyum, Valiant - 1985
48 Borel sets and circuit complexity (context) - Sipser - 1983
38 Languages which capture complexity classes (context) - Immerman - 1987
29 Logspace and logtime leaf languages - Jenner, McKenzie et al. - 1994
26 Polynomial and abstract subrecursive classes (context) - Mehlhorn - 1976
23 Reducibility by algebraic projections (context) - Valiant - 1982
18 Structural Complexity Theory (context) - Balc'azar, D'iaz et al. - 1988
14 A uniform approach to obtain diagonal sets in complexity cla.. (context) - Schoning - 1982
13 A note on structure and looking-back applied to the relative.. (context) - Chew, Machtey - 1981
12 An oracle characterization of the counting hierarchy (context) - Tor'an - 1988
12 On input read-modes of alternating Turing machines (context) - Cai, Chen - 1995
11 Algorithms for Boolean formula evaluation and for tree contr.. - Buss - 1993
10 Sublattices of the polynomial time degrees (context) - Ambos-Spies - 1985
8 On diagonalization methods and the structure of language cla.. (context) - Regan - 1983
8 The topology of provability in complexity theory (context) - Regan - 1988
7 The recursion-theoretic structure of complexity classes (context) - Schmidt - 1985
7 Independence results about context-free languages and lower .. (context) - Hartmanis - 1985
7 How to prove representation-independent independence results - Kurtz, O'Donnell et al. - 1987
6 Circuit bottom fan-in and computational power - Cai, Chen et al. - 1995
6 Reductions among polynomial isomorphism types (context) - Mahaney, Young - 1985
4 Polynomial time degrees of NP-sets (context) - Ambos-Spies - 1988
4 The gap-language technique revisited (context) - Vollmer - 1990
3 Three theorems on polynomial degrees of NP sets (context) - Ambos-Spies - 1985
3 and fixed-point theorems (context) - Regan, uniformity - 1992
3 the Separation of Complexity Classes (context) - Regan - 1986
3 Notes on log space representation (context) - Dowd - 1986
2 the structure of parametrized problems in NP (context) - Cai, Chen et al. - 1994
2 Minimum-complexity pairing functions (context) - Regan - 1992
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