Kolmogorov Complexity as a Language
نویسنده
چکیده
The notion of Kolmogorov complexity (=the minimal length of a program that generates some object) is often useful as a kind of language that allows us to reformulate some notions and therefore provide new intuition. In this survey we provide (with minimal comments) many different examples where notions and statements that involve Kolmogorov complexity are compared with their counterparts not involving complexity.
منابع مشابه
Kolmogorov Complexity of Categories
Kolmogorov complexity theory is used to tell what the algorithmic informational content of a string is. It is defined as the length of the shortest program that describes the string. We present a programming language that can be used to describe categories, functors, and natural transformations. With this in hand, we define the informational content of these categorical structures as the shorte...
متن کاملKolmogorov Complexity for Possibly Infinite Computations
In this paper we study the Kolmogorov complexity for non-effective computations, that is, either halting or non-halting computations on Turing machines. This complexity function is defined as the length of the shortest inputs that produce a desired output via a possibly non-halting computation. Clearly this function gives a lower bound of the classical Kolmogorov complexity. In particular, if t...
متن کاملA New Approach to Formal Language Theory by Kolmogorov Complexity
We present a new approach to formal language theory using Kolmogorov complexity. The main results presented here are an alternative for pumping lemma(s), a new characterization for regular languages, and a new method to separate deterministic context-free languages and nondeterministic context-free languages. The use of the new ‘incompressibility arguments’ is illustrated by many examples. The ...
متن کاملNatural Language Processing: Structure and Complexity
We introduce a method for analyzing the complexity of natural language processing tasks, and for predicting the difficulty new NLP tasks. Our complexity measures are derived from the Kolmogorov complexity of a class of automata — meaning automata, whose purpose is to extract relevant pieces of information from sentences. Natural language semantics is defined only relative to the set of question...
متن کاملOn Languages with Very High Information Content
The main result of this paper is the following: Any language in ESPACE that is bounded truthtable reducible in polynomial time to a set with very high space-bounded Kolmogorov complexity must be bounded truth-table reducible in polynomial time to a sparse set.
متن کامل