# 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…

## 15 Citations

### Reduction Techniques for Graph Isomorphism in the Context of Width Parameters

- MathematicsSWAT
- 2014

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

- Mathematics, Computer Sciencecomputational 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

- Computer Science, MathematicsSOFSEM
- 2009

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

- Mathematics, Computer Science
- 2007

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

- Mathematics, Computer Science
- 2007

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 *

- Mathematics
- 1996

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

- GeologySIGA
- 2014

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

- SociologySIGA
- 1994

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

- EducationSIGA
- 1998

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

- Computer Science, MathematicsFOCS
- 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.

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