Program Size Complexity for Possibly Infinite Computations

Abstract
We define a program size complexity function as a variant of the prefix-free Kolmogorov complexity, based on Turing monotone machines performing possibly unending computations. We consider definitions of randomness and triviality for sequences in relative to the complexity. We prove that the classes of Martin-Löf random sequences and -random sequences coincide and that the -trivial sequences are exactly the recursive ones. We also study some properties of and compare it with other complexity functions. In particular, is different from , the prefix-free complexity of monotone machines with oracle A
Keywords program size complexity   Kolmogorov complexity   infinite computations
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William C. Calhoun (2006). Degrees of Monotone Complexity. Journal of Symbolic Logic 71 (4):1327 - 1341.
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