Overview

In computational applications, an algorithm may solve a given problem, but be ""infeasible"" in practice because it requires large time and space resources. A ""feasible"" algorithm requires a ""small"" amount of time and/or memory and can be implemented on an abstract computational device such as a Turing machine or a boolean circuit. In investigating feasible algorithms, a wide variety of tools from combinatorics, logic, computational complexity theory and algebra can be employed. The purpose of the workshop on which this volume is based was to carry on the work of the first ""Feasible Mathematics"" workshop, held in 1989. Both workshops were held at Cornell University and sponsored by the University and Mathematics Sciences Institute. This volume contains contributions to feasible mathematics in three areas: computational complexity theory, proof theory and algebra, with substantial overlap between different fields. Among the topics covered are: boolean circuit lower bounds, novel characteristics of various boolean and sequential complexity classes, fixed-parameter tractability, higher order feasible functionals, higher order programs related to Plotkin's PCF, combinatorial proofs of feasible length, bounded arithmetic, feasible interpretations, polynomial time categoricity, and algebraic properties of finitely generated recursively enumerable algebras.

Full Product Details

Author:   Peter Clote ,  Jeffrey B. Remmel
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Edition:   1995 ed.
Volume:   13
Weight:   0.618kg
ISBN:  

9780817636753

ISBN 10:   0817636757
Pages:   447
Publication Date:   22 December 1994
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

Preface.- On the Existence of modulo p Cardinality Functions.- Predicative Recursion and The Polytime Hierarchy.- Are there Hard Examples for Frege Systems?.- On Godel’s Theorems on Lengths of Proofs II: Lower Bounds for Recognizing k Symbol Provability.- Feasibly Categorical Abelian Groups.- First Order Bounded Arithmetic and Small Boolean Circuit Complexity Classes.- Parameterized Computational Feasibility.- On Proving Lower Bounds for Circuit Size.- Effective Properties of Finitely Generated R.E. Algebras.- On Frege and Extended Frege Proof Systems.- Ramified Recurrence and Computational Complexity I: Word Recurrence and Poly-time.- Bounded Arithmetic and Lower Bounds in Boolean Complexity.- Ordinal Bounds for Programs.- Turing Machine Characterizations of Feasible Functionals of All Finite Types.- The Complexity of Feasible Interpretability.

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