Simulation Studies of Tornadic Vortices
John Case Principal Investigator
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Insightful characterizations of the power of various machine self- reference principles, both in the context of universal programming systems and clocked systems, are sought with an eye to determining what use is self-knowledge (for programs). It is expected that machine self-knowledge is useful for machine self-modification (learning). Characterizations or strong sufficient conditions are sought especially for those self-reference principles which are algebraically well- behaved. Conditions are sought for validity of the principle that, if there is no self-referential counterexample to a proposition, the proposition is true. A rigorous mathematical solution is sought to the problem of why machine self-reference proofs lay bare an underlying, simplest reason for the theorems they prove. In the context of machine learning theory the P.I. is studying the effects of imposing complexity and succinctness constraints on final programs and grammars learned, the power of (formal) language learning machines if they converge on a small, uniformly, bounded, finite number of grammars, and the relationship of these and other matters to separability by sets enumerable by effective procedures which, in effect, change their "minds" finitely often. The tradeoffs between complexity of subrecursive text and speed of the inference progress are being investigated. In relatively small community applying recursion theory in computer science the P.I. is regarded as a leading figure.