The Computational Complexity of Randomness

Reduction of Computational Complexity in Finite State Automata Explosion of Networked System Diagnosis (RESEARCH NOTE)

This research puts forward rough finite state automata which have been represented by two variants of BDD called ROBDD and ZBDD. The proposed structures have been used in networked system diagnosis and can overcome cominatorial explosion. In implementation the CUDD - Colorado University Decision Diagrams package is used. A mathematical proof for claimed complexity are provided which shows ZBDD ...

Algorithmic Information Theory and Kolmogorov Complexity

This document contains lecture notes of an introductory course on Kolmogorov complexity. They cover basic notions of algorithmic information theory: Kolmogorov complexity (plain, conditional, prefix), notion of randomness (Martin-Löf randomness, Mises–Church randomness), Solomonoff universal a priori probability and their properties (symmetry of information, connection between a priori probabil...

Round Complexity Versus Randomness Complexity in Interactive Proofs

Consider an interactive proof system for some set S that has randomness complexity r(n) for instances of length n, and arbitrary round complexity. We show a public-coin interactive proof system for S of round complexity O(r(n)/ log n). Furthermore, the randomness complexity is preserved up to a constant factor, and the resulting interactive proof system has perfect completeness. ∗Department of ...

Chaos/Complexity Theory and Education

Sciences exist to demonstrate the fundamental order underlying nature. Chaos/complexity theory is a novel and amazing field of scientific inquiry. Notions of our everyday experiences are somehow in connection to the laws of nature through chaos/complexity theory’s concerns with the relationships between simplicity and complexity, between orderliness and randomness (Retrieved from http://www.inc...

Structures et aléa en finance, une approche par la complexité algorithmique de l'information. (Structures and randomness on finance, an approach by computational complexity theory)