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Abstract: The study of the complexity of sets encompasses two complementary aims: (1) establishing -- usually via explicit construction of algorithms -- that sets are feasible, and (2) studying the relative complexity of sets that plausibly might be feasible but are not currently known to be feasible (such as the NP-complete sets and the PSPACE-complete sets). For the study of the complexity of closure properties, a recent urry of results [21, 33, 49, 6, 7, 16] has established an analog of (1); these... (Update)
Context of citations to this paper: More
.... of closure properties for complexity classes of functions was established Preprint submitted to Elsevier Preprint 22 November 1999 in [8]. A class F is closed under f if the composition of f with any function in F is again a function in F . Of highest importance are (non...
.... improve the lower bound beyond UP O(1) and they show that relativizable techniques cannot raise the UP O(1) hardness lower bound to SPP [OH93,FFK94] the gap analog of UP. In particular, they note that if every nontrivial counting property of circuits is SPP hard then SPP ....
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BibTeX entry: (Update)
M. Ogiwara and L. A. Hemachandra. A complexity theory of feasible closure properties. In Proceedings of the 6th Annual IEEE Structure in Complexity Theory Conference, pages 16--29, 1991. http://citeseer.ist.psu.edu/ogiwara91complexity.html More
@inproceedings{ ogiwara91complexity,
author = "Mitsunori Ogiwara and Lane A. Hemachandra",
title = "A Complexity Theory for Feasible Closure Properties",
booktitle = "Structure in Complexity Theory Conference",
pages = "16--29",
year = "1991",
url = "citeseer.ist.psu.edu/ogiwara91complexity.html" }
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1911 Introduction to Automata Theory (context) - Hopcroft, Ullman - 1979
534 The complexity of theorem-proving procedures (context) - Cook - 1971
163 The complexity of enumeration and reliability problems (context) - Valiant - 1979
151 The complexity of optimization problems (context) - Krentel - 1988
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129 Theoretical Computer Science (context) - Stockmeyer, hierarchy - 1977
122 A comparison of polynomial time reducibilities (context) - Ladner, Lynch et al. - 1975
107 complete approximation problems (context) - Sahni, Gonzalez - 1976
94 the structure of polynomial time reducibility (context) - Ladner - 1975
70 The boolean hierarchy I: Structural properties (context) - Cai, Gundermann et al. - 1988
66 PP is closed under intersection - Beigel, Reingold et al. - 1991
56 Information Processing Letters (context) - Valiant, complexity et al. - 1976
55 On Some Central Problems in Computational Complexity (context) - Simon - 1975
53 Counting classes are at least as hard as the polynomial-time.. (context) - Toda, Ogiwara - 1991
45 Two remarks on the power of counting (context) - Papadimitriou, Zachos - 1983
44 Problems of Information Transmission (context) - Levin, problems - 1973
44 the power of parity polynomial time (context) - Cai, Hemachandra - 1990
38 PP is closed under truth-table reductions - Fortnow, Reingold - 1991
37 Counting classes: Thresholds (context) - Beigel, Gill et al. - 1990
36 Recognizing primes in random polynomial time (context) - Adleman, Huang - 1987
35 The boolean hierarchy II: Applications (context) - Cai, Gundermann et al. - 1989
32 Computationally related problems (context) - Sahni - 1974
31 Lower bounds for the low hierarchy - Allender, Hemachandra
30 the construction of parallel computers from various bases of.. (context) - Goldschlager, Parberry - 1986
26 A survey of counting classes (context) - Gundermann, Nasser et al. - 1990
23 and the polynomial hierarchy (context) - Beigel, threshold - 1989
19 Probabilistic polynomial time is closed under parity reducti.. - Beigel, Hemachandra et al. - 1991
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13 Structural Properties of the Counting Hierarchies (context) - Tor - 1988
13 Gap-denable counting classes (context) - Fenner, Fortnow et al. - 1990
12 An oracle characterization of the counting hierarchy (context) - Tor - 1988
12 A complexity theory for closure properties (context) - Ogiwara, Hemachandra - 1990
12 Probabilistic complexity classes and lowness (context) - Sch - 1987
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8 Turing machines with few accepting computations and low sets.. (context) - obler, Sch et al. - 1989
8 the computational power of exact counting (context) - Ogiwara - 1990
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2 A low and a high hierarchy in NP (context) - Sch - 1983
2 Characterizing low levels of the polynomial-time hierarchy r.. (context) - Ogiwara - 1991
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1 A note on structure and looking back applied to the complexi.. (context) - Chew, Machtey - 1981
1 Enumeration problems (context) - Regan - 1982
1 The complexity of nding medians (context) - Toda - 1990
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.cs.rochester.edu/users/faculty/ogihara/research/CCC/ccc.html): More
On Helping by Parity-like Languages - Ogihara (1994) (Correct)
Sparse Sets versus Complexity Classes - Cai, Ogihara (1996) (Correct)
Computing Solutions Uniquely Collapses the Polynomial.. - Hemaspaandra, Naik.. (1996) (Correct)
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