Complexity Theory Retrospective

  title={Complexity Theory Retrospective},
  author={Juris Hartmanis},
  booktitle={Springer New York},
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

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
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

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

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

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 *

Bags, i.e., sets with duplicates, are often used to implement relations in database systems. In this paper, we study the expressive power of algebras for manipulating bags. The algebra we present is

Beautiful structures: an appreciation of the contributions of Alan Selman

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.

Teaching Computational Complexity: Resources to Treasure

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

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
  • 1998
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.



Complete problems, creative sets and isomorphism conjectures

In 1977, Berman and Hartmanis proved that all the known NP-complete sets are essentially the same: $p$-isomorphic. Based on this evidence, they conjectured that all the NP-complete sets are

A note on one-way functions and polynomial-time isomorphisms

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.

A Note on Sparse Complete Sets

  • S. Fortune
  • Mathematics, Computer Science
    SIAM J. Comput.
  • 1979
It is shown that the existence of an NP- complete set whose complement is sparse implies P = NP, and that if there is a polynomial time reduction with sparse range to a PTAPE-complete set, then P=PTAPE.

Three results on the polynomial isomorphism of complete sets

  • J. GoldsmithD. Joseph
  • Mathematics
    27th Annual Symposium on Foundations of Computer Science (sfcs 1986)
  • 1986
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.

One-way functions, robustness, and the non-isomorphism of NP-complete sets

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?

Kolmogorov complexity and degrees of tally sets

  • E. AllenderO. Watanabe
  • Mathematics
    [1988] Proceedings. Structure in Complexity Theory Third Annual Conference
  • 1988
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