unconventional algorithms complementarity of axiomatics and construction非常规算法互补的公理系统和建设.pdf

Entropy 2012, 14, 2066-2080; doi:10.3390/ OPEN ACCESS entropy ISSN 1099-4300 /journal/entropy Article Unconventional Algorithms: Complementarity of Axiomatics and Construction Gordana Dodig Crnkovic 1,* and Mark Burgin 2 1 Department of Computer Science and Networks, School of Innovation, Design and Engineering Mälardalen University, Västerås, 72123, Sweden 2 Department of Mathematics, UCLA, Los Angeles, CA 90095, USA; E-Mail: mburgin@ (M.B.) * Author to whom correspondence should be addressed; E-Mail: gordana.dodig-crnkovic@mdh.se; Tel.: +46 21 15 17 25. Received: 20 August 2012; in revised form: 23 September 2012; / Accepted: 19 October 2012 / Published: 25 October 2012 Abstract: In this paper, we analyze axiomatic and constructive issues of unconventional computations from a methodological and philosophical point of view. We explain how the new models of algorithms and unconventional computations change the algorithmic universe, making it open and allowing increased flexibility and expressive power that augment creativity. At the same time, the greater power of new types of algorithms also results in the greater complexity of the algorithmic universe, transforming it into the algorithmic multiverse and demanding new tools for its study. That is why we analyze new powerful tools brought forth by local mathematics, local logics, logical varieties and the axiomatic theory of algorithms, automata and computation. We demonstra