Complexity Theory Retrospective

@inproceedings{Hartmanis1990ComplexityTR,
  title={Complexity Theory Retrospective},
  author={Juris Hartmanis},
  booktitle={Springer New York},
  year={1990}
}
In this paper we survey Juris Hartmanis' contributions to isomorphism problems. These problems are primarily of two forms. First, isomorphism problems for restricted programming systems, including the Harimanis-Baker conjecture that all polynomial time programming systems are polynomially isomorphic. Second, the research on isomorphisms, and particularly polynomial time isomorphisms for complete problems for various natural complexity classes, including the Berman-Hartmanis conjecture that all… 

Reduction Techniques for Graph Isomorphism in the Context of Width Parameters

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An fpt Turing-reduction from strong tree width to the a priori unrelated parameter maximum degree is developed and shown as a possibly first step towards intractability results for parameterized graph isomorphism.

On a Theorem of Razborov

  • H. Wunderlich
  • Mathematics, Computer Science
    computational complexity
  • 2011
TLDR
It turns out that Razborov's astounding result is actually a corollary of a slight generalization of Toda’s First Theorem in communication complexity and that matrix rigidity over a finite field is a lower-bound method for bounded-error modular communication complexity.

On Toda's Theorem in Structural Communication Complexity

TLDR
Toda's Theorem is proved, i.e. every language in this class can be decided with alternating protocols using $\mathcal{O}(\log n/\log\log n)$ many alternations.

Collapsing Polynomial-Time

TLDR
This work has been able to construct a recursive set such that its bounded truth-table degree collapses to its many-one degree and shows that such a set { if it exists { must be recursive.

Collapsing Polynomial-Time Degrees

TLDR
The question whether there is a set such that its Turing degree collapses to its many-one degree is still open; however, it is shown that such a set – if it exists – must be recursive.

Towards Tractable Algebras for Bags *

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Beautiful structures: an appreciation of the contributions of Alan Selman

TLDR
This article is an appreciation, on the occasion of his retirement, of some of the most lovely concepts and results that Alan has contributed to the field.

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This article describes and discusses textbooks, monographs, and collections that are excellent resources from which to teach courses on computational complexity theory.

Writing and editing complexity theory: tales and tools

TLDR
In this article, a number of the excellent resources available to writers and editors are listed, and some of the adventures the author had as her book moved from concept to reality are related.

Quantum Oracle Interrogation: Getting All Information for Almost Half the Price

  • W. V. Dam
  • Computer Science, Mathematics
    FOCS
  • 1998
TLDR
It follows that any function with the N bits of the oracle as input can be calculated using N/2+/spl radic/N queries if the authors allow a small probability of error.

References

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TLDR
It is conjectured in [5,8] that if one-way functions exist, then not all NP-complete sets are polynomial-time isomorphic, which is difficult since it implies that P ~ NP.

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TLDR
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TLDR
This paper proves three results relating to the isomorphism question for NP-complete sets, showing that no simple modification of the diagonalization argument used by Ko, Long and Du can be used to produce sets that are both EXPtime-complete w.r.t, polynomial many-one reducibility and not p-isomorphic.

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TLDR
It is established that in relativized worlds there are NP-complete sets that are non-isomorphic in a strong sense and proves that robust machines squander their powerful nondeterministic oracle access in all relativizations.

Does co-NP Have Short Interactive Proofs?

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    [1988] Proceedings. Structure in Complexity Theory Third Annual Conference
  • 1988
TLDR
The authors investigate some of these questions and show that they are equivalent to each other and are closely related to other important open questions in complexity theory.

On Counting Problems and the Polynomial-Time Hierarchy

Collapsing degrees

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