Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
A connotational theory of program structure
A connotational theory of program structure
The formal semantics of programming languages: an introduction
The formal semantics of programming languages: an introduction
Subrecursive programming systems: complexity & succinctness
Subrecursive programming systems: complexity & succinctness
A Machine-Independent Theory of the Complexity of Recursive Functions
Journal of the ACM (JACM)
Control structures in hypothesis spaces: the influence on learning
Theoretical Computer Science
An Introduction to the General Theory of Algorithms
An Introduction to the General Theory of Algorithms
A Guided Tour Across the Boundaries of Learning Recursive Languages
Algorithmic Learning for Knowledge-Based Systems, GOSLER Final Report
The independence of control structures in abstract programming systems
The independence of control structures in abstract programming systems
Properties complementary to program self-reference
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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The interest is in characterizing insightfully the power of program self-reference in effective programming systems (epses), the computability-theoretic analogs of programming languages. In an epsin which the constructiveform of Kleene's Recursion Theorem (KRT) holds, it is possible to construct, algorithmically, from an arbitrary algorithmic task, a self-referential program that, in a sense, creates a self-copy and then performs that task on the self-copy. In an epsin which the not-necessarily-constructive form of Kleene's Recursion Theorem (krt) holds, such self-referential programs exist, but cannot, in general, be found algorithmically.In an earlier effort, Royer proved that there is nocollection of recursive denotational control structures whose implementability characterizesthe epses in which KRTholds. One main result herein, proven by a finite injury priority argument, is that the epses in which krtholds are, similarly, notcharacterized by the implementability of some collection of recursive denotational control structures.On the positive side, however, a characterization of such epses of a rather different sort isshown herein. Though, perhaps not the insightful characterization sought after, this surprising result reveals that a hidden and inherent constructivity is always present in krt.Know thyself.--- Greek proverb