E. Allender | Semantic Scholar

E. Allender, M. Loui, Kenneth W. Regan
Computer Science
Encyclopedia of Cryptography and Security
1997

In this chapter, P, NP, and related complexity classes are defined, and the use of diagonalization and padding techniques to prove relationships between classes are illustrated, and it is shown how to prove that a problem is NP-complete.

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On the complexity of numerical analysis

E. Allender, Peter Bürgisser, Johan Kjeldgaard-Pedersen, Peter Bro Miltersen
Mathematics
21st Annual IEEE Conference on Computational…
16 July 2006

It is shown that the Euclidean traveling salesman problem lies in the counting hierarchy - the previous best upper bound for this important problem (in terms of classical complexity classes) being PSPACE.

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Non-Commutative Arithmetic Circuits: Depth Reduction and Size Lower Bounds

E. Allender, Jia Jiao, M. Mahajan, V. Vinay
Mathematics, Computer Science
Theor. Comput. Sci.
7 February 1996

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Uniform constant-depth threshold circuits for division and iterated multiplication

W. Hesse, E. Allender, D. M. Barrington
Computer Science, Mathematics
J. Comput. Syst. Sci.
1 December 2002

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The complexity of matrix rank and feasible systems of linear equations

E. Allender, R. Beals, M. Ogihara
Computer Science
STOC '96
1 July 1996

It is shown that this natural complexity class for which the problems of determining if a system of linear equations is feasible and computing the rank of an integer matrix are complete under logspace reductions is closed under NC1-reducibility.

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A note on the power of threshold circuits

E. Allender
Computer Science
30th Annual Symposium on Foundations of Computer…
30 October 1989

The author presents a very simple proof of the fact that any language accepted by polynomial-size depth-k unbounded-fan-in circuits of AND and OR gates is accepted by depth-three threshold circuits…

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The complexity of satisfiability problems: Refining Schaefer's theorem

E. Allender, Michael Bauland, N. Immerman, Henning Schnoor, H. Vollmer
Mathematics
J. Comput. Syst. Sci.
29 August 2005

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The Permanent Requires Large Uniform Threshold Circuits

E. Allender
Computer Science
Chic. J. Theor. Comput. Sci.
1999

It is shown that the permanent cannot be computed by uniform constantdepth threshold circuits of size T (n), for any function T such that for all k, T ( n) = o(2), and any problem that is hard for the complexity class C=P requires circuits of this size.

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Complexity of finite-horizon Markov decision process problems

M. Mundhenk, J. Goldsmith, Christopher Lusena, E. Allender
Computer Science, Mathematics
JACM
1 July 2000

This work analyzes the computational complexity of evaluating policies and of determining whether a sufficiently good policy exists for a Markov decision process, based on a number of confounding factors, including the observability of the system state; the succinctness of the representation; the type of policy; even the number of actions relative to theNumber of states.

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Measure on small complexity classes, with applications for BPP

E. Allender, M. Strauss
Computer Science
Proceedings 35th Annual Symposium on Foundations…
20 November 1994

A notion of resource-bounded measure for P and other subexponential-time classes is presented, based on Lutz's notion of measure, but overcomes the limitations that cause Lutz’s definitions to apply only to classes at least as large as E.

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