Feasible Mathematics
A Mathematical Sciences Institute Workshop, Ithaca, New York, June 1989

Editors: Samuel R. Buss, Philip J. Scott



A so-called "effective" algorithm may require arbitrarily large finite amounts of time and space resources, and hence may not be practical in the real world. A "feasible" algorithm is one which only requires a limited amount of space and/or time for execution; the general idea is that a feasible algorithm is one which may be practical on today's or at least tomorrow's computers. There is no definitive analogue of Church's thesis giving a mathematical definition of feasibility; however, the most widely studied mathematical model of feasible computability is polynomial-time computability. Feasible Mathematics includes both the study of feasible computation from a mathematical and logical point of view and the reworking of traditional mathematics from the point of view of feasible computation. The diversity of Feasible Mathematics is illustrated by the. contents of this volume which includes papers on weak fragments of arithmetic, on higher type functionals, on bounded linear logic, on sub recursive definitions of complexity classes, on finite model theory, on models of feasible computation for real numbers, on vector spaces and on recursion theory. The vVorkshop on Feasible Mathematics was sponsored by the Mathematical Sciences Institute and was held at Cornell University, June 26-28, 1989.

Table of contents (18 chapters)

Front Matter

Parity and the Pigeonhole Principle

Computing over the Reals (or an Arbitrary Ring)

On Model Theory for Intuitionistic Bounded Arithmetic with Applications to Independence Results

Sequential, machine-independent characterizations of the parallel complexity classes AlogTIME, AC k , NC k and NC

Characterizations of the Basic Feasible Functionals of Finite Type

Functional Interpretations of Feasibly Constructive Arithmetic Abstract

Polynomial-time combinatorial operators are polynomials

Isols and Kneser Graphs

Stockmeyer induction

Probabilities of sentences about two linear orderings

Bounded Linear Logic: A Modular Approach to Polynomial Time Computability

On Finite Model Theory (Extended Abstract)

Computational Models For Feasible Real Analysis

Inverting a One-to-One Real Function Is Inherently Sequential

On Bounded ∑ 1 1 Polynomial Induction

Subrecursion and lambda representation over free algebras

Complexity-Theoretic Algebra: Vector Space Bases

When is every recursive linear ordering of type μ recursively isomorphic to a polynomial time linear ordering over the natural numbers in binary form?

Back Matter


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