A Generalized Quantifier Concept in Computational Complexity Theory

Authors:
Heribert Vollmer
Affiliations:
-
Venue:
ESSLLI '97 Revised Lectures from the 9th European Summer School on Logic, Language, and Information: Generalized Quantifiers and Computation
Year:
1997

Citing 38
Cited 0

Separating the polynomial-time hierarchy by oracles

Proc. 26th annual symposium on Foundations of computer science
The complexity of combinatorial problems with succinct input representation

Acta Informatica
Some observations on the connection between counting and recursion

Theoretical Computer Science
Two characterizations of the logarithmic alternation hierarchy

Proceedings of the 12th symposium on Mathematical foundations of computer science 1986
Finite monoids and the fine structure of NC1

Journal of the ACM (JACM)
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1

Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Expressibility and parallel complexity

SIAM Journal on Computing
On uniformity within NC1

Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
PP is closed under intersection

STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
A catalog of complexity classes

Handbook of theoretical computer science (vol. A)
Complexity classes defined by counting quantifiers

Journal of the ACM (JACM)
PP is as hard as the polynomial-time hierarchy

SIAM Journal on Computing
A uniform approach to define complexity classes

Theoretical Computer Science
The complexity of algorithmic problems on succinct instances

Computer science
Using the Hamiltonian path operator to capture NP

Journal of Computer and System Sciences
Introduction to the theory of complexity

Introduction to the theory of complexity
Finite automata, formal logic, and circuit complexity

Finite automata, formal logic, and circuit complexity
On input read-modes of alternating Turing machines

Theoretical Computer Science
On the acceptance power of regular languages

STACS '94 Selected papers of the eleventh symposium on Theoretical aspects of computer science
Succinct circuit representations and leaf language classes are basically the same concept

Information Processing Letters
Gap-languages and log-time complexity classes

Theoretical Computer Science
Counting complexity

Complexity theory retrospective II
Automata, Languages, and Machines

Automata, Languages, and Machines
Handbook of Formal Languages

Handbook of Formal Languages
On Type-2 Probabilistic Quantifiers

ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
A Note on Uniform Circuit Lower Bounds for the Counting Hierarchy (Extended Abstract)

COCOON '96 Proceedings of the Second Annual International Conference on Computing and Combinatorics
Oracles and Quantifiers

CSL '93 Selected Papers from the 7th Workshop on Computer Science Logic
Logics Capturing Relativized Complexity Classes Uniformly

LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
Relations Among Parallel and Sequential Computation Models

ASIAN '96 Proceedings of the Second Asian Computing Science Conference on Concurrency and Parallelism, Programming, Networking, and Security
Relativized Logspace and Generalized Quantifiers Over Finite Structures

LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Succinct Representation, Leaf Languages, and Projection Reductions

CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Nondeterministic NC1 Computation

CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
The General Notion of a Dot-Operator

CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Acceptance by Transformation Monoids (with an Application to Local Self Reductions)

CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
On Operators of Higher Types

CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Word problems requiring exponential time(Preliminary Report)

STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Borel sets and circuit complexity

STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
On the power of number-theoretic operations with respect to counting

SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)

Quantified Score

Hi-index	0.00

Visualization

Abstract

A notion of generalized quantifier in computational complexity theory is explored and used to give a unified treatment of leaf language definability, oracle separations, type 2 operators, and circuits with monoidal gates. Relations to Lindström quantifiers are pointed out.