Simulation Studies of Tornadic Vortices

在通用编程系统和时钟系统的背景下，对各种机器自我参考原理的能力进行深刻的描述，以确定自我知识（对程序）的用途。人们期望机器的自知识能够用于机器的自修改（学习）。特别是对于那些代数上表现良好的自参照原理，寻求表征或强充分条件。如果一个命题没有自我指涉的反例，那么这个命题就是真的，这一原则的有效性需要寻找条件。一个严格的数学解决方案是寻求为什么机器自我引用证明揭示了一个潜在的，最简单的原因，他们所证明的定理的问题。在机器学习理论的背景下，P.I.正在研究对最终程序和所学语法施加复杂性和简洁性约束的影响，（正式）语言学习机器的力量，如果它们收敛于一个小的、一致的、有界的、有限数量的语法，以及这些和其他事项与可分性的关系，这些可分性是由有效程序可枚举的集合组成的，实际上，经常改变他们的“想法”。研究了子递归文本复杂性与推理速度之间的权衡关系。在将递归理论应用于计算机科学的相对较小的群体中，pi被视为领军人物。

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.