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Binary Lambda Calculus and Combinatory Logic.” Sep 14, 2004. http://homepages. cwi.nl/ ∼ tromp/cl/LC.pdf [64] Tadaki, K. “Upper bound by Kolmogorov complexity for the probability
- in computable POVM measurement.” Proceedings of the 5th Conference on Real Numbers and Computers, RNC5
, 2003
"... In the first part, we introduce binary representations of both lambda calculus and combinatory logic terms, and demonstrate their simplicity by providing very compact parser-interpreters for these binary languages. Along the way we also present new results on list representations, bracket abstractio ..."
Abstract
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Cited by 3 (0 self)
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In the first part, we introduce binary representations of both lambda calculus and combinatory logic terms, and demonstrate their simplicity by providing very compact parser-interpreters for these binary languages. Along the way we also present new results on list representations, bracket abstraction, and fixpoint combinators. In the second part we review Algorithmic Information Theory, for which these interpreters provide a convenient vehicle. We demonstrate this with several concrete upper bounds on program-size complexity, including an elegant self-delimiting code for binary strings. 1
Kolmogorov Complexity in Combinatory Logic
"... Intuitively, the amount of information in a string is the size of the shortest program that outputs the string. The first billion digits of # for example, contain very little information, since they can be calculated by a C program of a few lines only. Although information content seems to be hi ..."
Abstract
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Intuitively, the amount of information in a string is the size of the shortest program that outputs the string. The first billion digits of # for example, contain very little information, since they can be calculated by a C program of a few lines only. Although information content seems to be highly dependent on choice of programming language, the notion is actually invariant up to an additive constant.
