Proceedings ArticleDOI
Parity, circuits, and the polynomial-time hierarchy
Merrick L. Furst,James B. Saxe,Michael Sipser +2 more
- pp 260-270
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A super-polynomial lower bound is given for the size of circuits of fixed depth computing the parity function and connections are given to the theory of programmable logic arrays and to the relativization of the polynomial-time hierarchy.Abstract:
A super-polynomial lower bound is given for the size of circuits of fixed depth computing the parity function. Introducing the notion of polynomial-size, constant-depth reduction, similar results are shown for the majority, multiplication, and transitive closure functions. Connections are given to the theory of programmable logic arrays and to the relativization of the polynomial-time hierarchy.read more
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Elements of Finite Model Theory
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Journal ArticleDOI
Parity, circuits and the polynomial time hierarchy
TL;DR: A super-polynomial lower bound is given for the size of circuits of fixed depth computing the parity function and connections are given to the theory of programmable logic arrays and to the relativization of the polynomial-time hierarchy.
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References
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The polynomial-time hierarchy☆
TL;DR: The problem of deciding validity in the theory of equality is shown to be complete in polynomial-space, and close upper and lower bounds on the space complexity of this problem are established.
Proceedings ArticleDOI
Word problems requiring exponential time(Preliminary Report)
L. J. Stockmeyer,A. R. Meyer +1 more
TL;DR: A number of similar decidable word problems from automata theory and logic whose inherent computational complexity can be precisely characterized in terms of time or space requirements on deterministic or nondeterministic Turing machines are considered.
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Relativizations of the $\mathcal{P} = ?\mathcal{NP}$ Question
TL;DR: Relativized versions of the open question of whether every language accepted nondeterministically in polynomial time can be recognized deterministic in poynomial time are investigated.
Journal ArticleDOI
Relativization of questions about log space computability
Richard E. Ladner,Nancy Lynch +1 more
TL;DR: A notion of log space Turing reducibility is introduced and it is shown that there exists a computable setA such that and.
Journal ArticleDOI
A second step toward the polynomial hierarchy
Theodore P. Baker,Alan L. Selman +1 more
TL;DR: The principal result is that there exists a recursive oracle for which the relativized polynomial hierarchy exists through the second level; that is, there is a recursive set B such that Σ2P,B ≠ π2 P,B.