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FiniteModel Theory  A Personal Perspective
 Theoretical Computer Science
, 1993
"... Finitemodel theory is a study of the logical properties of finite mathematical structures. This paper is a very personalized view of finitemodel theory, where the author focuses on his own personal history, and results and problems of interest to him, especially those springing from work in his Ph ..."
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Cited by 20 (0 self)
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Finitemodel theory is a study of the logical properties of finite mathematical structures. This paper is a very personalized view of finitemodel theory, where the author focuses on his own personal history, and results and problems of interest to him, especially those springing from work in his Ph.D. thesis. Among the topics discussed are:
Limitations of the Upward Separation Technique
, 1990
"... this paper was presented at the 16th International Colloquium on Automata, Languages, and Programming [3] ..."
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Cited by 16 (0 self)
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this paper was presented at the 16th International Colloquium on Automata, Languages, and Programming [3]
Circuit size relative to pseudorandom oracles, Theoretical Computer Science A 107
, 1993
"... Circuitsize complexity is compared with deterministic and nondeterministic time complexity in the presence of pseudorandom oracles. The following separations are shown to hold relative to every pspacerandom oracle A, and relative toalmost every oracle A 2 ESPACE. (i) NP A is not contained in SIZE ..."
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Cited by 15 (4 self)
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Circuitsize complexity is compared with deterministic and nondeterministic time complexity in the presence of pseudorandom oracles. The following separations are shown to hold relative to every pspacerandom oracle A, and relative toalmost every oracle A 2 ESPACE. (i) NP A is not contained in SIZE A (2 n)foranyreal < 1 3. (ii) E A is not contained in SIZE A ( 2n n). Thus, neither NP A nor E A is contained in P A /Poly. In fact, these separations are shown to hold for almost every n. Since a randomly selected oracle is pspacerandom with probability one, (i) and (ii) immediately imply the corresponding random oracle separations, thus improving a result of Bennett and Gill [9] and answering open questions of Wilson [47]. 1