Programming languages capturing complexity classes

Authors:
Lars Kristiansen;Paul J. Voda
Affiliations:
Oslo University College, Faculty of Engineering, Olavs Plass, Oslo, Norway and Department of Mathematics, University of Oslo, Blindern, Oslo, Norway;Institute of Informatics, Comenius University Bratislava, Bratislava, Slovakia
Venue:
Nordic Journal of Computing
Year:
2005

Citing 13
Cited 5

Characterizing complexity classes by higher type primitive recursive definitions

Theoretical Computer Science
A new recursion-theoretic characterization of the polytime functions

Computational Complexity
Computability and complexity: from a programming perspective

Computability and complexity: from a programming perspective
LOGSPACE and PTIME characterized by programming languages

Theoretical Computer Science - Special issue on mathematical foundations of programming semantics
Ranking Primitive Recursions: The Low Grzegorczyk Classes Revisited

SIAM Journal on Computing
Elements of the Theory of Computation

Elements of the Theory of Computation
Characterizing Complexity Classes by Higher Type Primitive Recursive Definitions, Part II

Proceedings of the 6th International Meeting of Young Computer Scientists on Aspects and Prospects of Theoretical Computer Science
Intrinsic Theories and Computational Complexity

LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
Complexity classes and fragments of C

Information Processing Letters
The expressive power of higher-order types or, life without CONS

Journal of Functional Programming
On the computational complexity of imperative programming languages

Theoretical Computer Science - Implicit computational complexity
Neat function algebraic characterizations of logspace and linspace

Computational Complexity
The small grzegorczyk classes and the typed λ-calculus

CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms

Recursion in Higher Types and Resource Bounded Turing Machines

CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
A flow calculus of mwp-bounds for complexity analysis

ACM Transactions on Computational Logic (TOCL)
The structure of detour degrees

TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Complexity-Theoretic hierarchies

CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
The trade-off theorem and fragments of Gödel’s T

TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

We investigate an imperative and a functional programming language. The computational power of fragments of these languages induce two hierarchies of complexity classes. Our first main theorem says that these hierarchies match, level by level, a complexity-theoretic alternating space-time hierarchy known from the literature. Our second main theorems says that a slightly different complexity-theoretic hierarchy (the Goerdt-Seidl hierarchy) also can be captured by hierarchies induced by fragments of the programming languages. Well known complexity classes like LOGSPACE, LINSPACE, P, PSPACE, etc., occur in the hierarchies.