Feasible Mathematics II

Editors: Peter Clote, Jeffrey B. Remmel



Perspicuity is part of proof. If the process by means of which I get a result were not surveyable, I might indeed make a note that this number is what comes out - but what fact is this supposed to confirm for me? I don't know 'what is supposed to come out' . . . . 1 -L. Wittgenstein A feasible computation uses small resources on an abstract computa- tion device, such as a 'lUring machine or boolean circuit. Feasible math- ematics concerns the study of feasible computations, using combinatorics and logic, as well as the study of feasibly presented mathematical structures such as groups, algebras, and so on. This volume contains contributions to feasible mathematics in three areas: computational complexity theory, proof theory and algebra, with substantial overlap between different fields. In computational complexity theory, the polynomial time hierarchy is characterized without the introduction of runtime bounds by the closure of certain initial functions under safe composition, predicative recursion on notation, and unbounded minimization (S. Bellantoni); an alternative way of looking at NP problems is introduced which focuses on which pa- rameters of the problem are the cause of its computational complexity and completeness, density and separation/collapse results are given for a struc- ture theory for parametrized problems (R. Downey and M. Fellows); new characterizations of PTIME and LINEAR SPACE are given using predicative recurrence over all finite tiers of certain stratified free algebras

Table of contents (15 chapters)

Front Matter

On the Existence of modulo p Cardinality Functions

Predicative Recursion and The Polytime Hierarchy

Are there Hard Examples for Frege Systems?

On Gödel’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



Feasible Mathematics I 下载地址：
https://bbs.pinggu.org/thread-4932789-1-1.html