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雷达卡
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
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