Several results in program size complexity

LISP Program - Size Complexity II

We present the information-theoretic incompleteness theorems that arise in a theory of program-size complexity based on something close to real LISP. The complexity of a formal axiomatic system is defined to be the minimum size in characters of a LISP definition of the proofchecking function associated with the formal system. Using this concrete and easy to understand definition, we show (a) th...

Program Size Complexity for Possibly Infinite Computations

We define a program size complexity function H∞ 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 {0, 1} relative to the H∞ complexity. We prove that the classes of Martin-Löf random sequences and H∞-random sequences coincide, and that the H∞-tr...

Program-size Complexity Computes the Halting Problem

Shape and Size Relationship of Several Lunar Dusts: Preliminary Results

Introduction: Before establishing a human outpost on the Moon, numerous problems associated with lunar dust must be addressed and mitigated [1, 2]. The deleterious nature of lunar dusts was experienced during all Apollo missions. Lunar dusts (brought in on dirty spacesuits and boots) contaminated the atmosphere in the lunar module and irritated the eyes, sinuses, and throats of the astronauts [...

The Program-Size Complexity of Self-Assembled Squares

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