• Publications
  • Influence
On the complexity of numerical analysis
TLDR
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. Expand
Complexity Theory
TLDR
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. Expand
Non-Commutative Arithmetic Circuits: Depth Reduction and Size Lower Bounds
TLDR
It is proved that in the commutative setting, uniform semi-unbounded arithmetic circuits of logarithmic depth are as powerful as uniform arithmetic circuit of polynomial degree (and unrestricted depth); earlier proofs did not work in the uniform setting. Expand
The Permanent Requires Large Uniform Threshold Circuits
  • E. Allender
  • Mathematics, Computer Science
  • Chic. J. Theor. Comput. Sci.
  • 1999
TLDR
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. Expand
Uniform constant-depth threshold circuits for division and iterated multiplication
TLDR
It is shown that division lies in the complexity class FOM + POW obtained by augmenting FOM with a predicate for powering modulo small primes, and that the predicate POW itself lies in FOM. Expand
A note on the power of threshold circuits
  • E. Allender
  • Mathematics, 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 circuitsExpand
The complexity of matrix rank and feasible systems of linear equations
TLDR
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. Expand
Measure on small complexity classes, with applications for BPP
  • E. Allender, M. Strauss
  • Computer Science, Mathematics
  • Proceedings 35th Annual Symposium on Foundations…
  • 20 November 1994
TLDR
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. Expand
Making Nondeterminism Unambiguous
TLDR
It is shown that in the context of nonuniform complexity, nondeterministic logarithmic space bounded computation can be made unambiguous in the class of problems reducible to context-free languages. Expand
Relationships Among PL, #L, and the Determinant
TLDR
A very simple proof of theorem of Jung is given, showing that probabilistic logspace-bounded (PL) machines lose none of their computational power if they are restricted to run in polynomial time. Expand
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