Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Toward a Theory of Enumerations
Journal of the ACM (JACM)
Optimization Among Provably Equivalent Programs
Journal of the ACM (JACM)
An Introduction to the General Theory of Algorithms
An Introduction to the General Theory of Algorithms
Relations between diagonalization, proof systems, and complexity gaps
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Some connections between mathematical logic and complexity theory
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
A programming language theorem which is independent of Peano Arithmetic
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
A Constructive Theory of Recursive Functions
A Constructive Theory of Recursive Functions
Independence results in computer science
ACM SIGACT News
The Expressiveness of Simple and Second-Order Type Structures
Journal of the ACM (JACM)
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
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Although there has been considerable additional work discussing limitations of formal proof techniques for Computer Science ([YO-73&77], [HAR-76], [HAR&HO-77], [HAJ-77&79], [GO-79]), these papers show only very general consequences of incompleteness: the stated results hold for all sufficiently powerful formal systems for Computer Science. Only the work of O'Donnell and of Lipton directly addresses the question of just how powerful formal axioms for Computer Science should be, and these two authors make rather radically different suggestions. We investigate this latter question: How powerful should a set of axioms be if it is to be adequate for Computer Science? In particular, in this paper we investigate the adequacy of the system of [LI-78] as a formal system for Computer Science.