Feasible Mathematics II

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.