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Entropy 2012, 14(11), 2066-2080; doi:10.3390/e14112066

Unconventional Algorithms: Complementarity of Axiomatics and Construction

Department of Computer Science and Networks, School of Innovation, Design and Engineering Mälardalen University, Västerås, 72123, Sweden
Department of Mathematics, UCLA, Los Angeles, CA 90095, USA
Author to whom correspondence should be addressed.
Received: 20 August 2012 / Accepted: 19 October 2012 / Published: 25 October 2012
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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 demonstrate how these new tools allow efficient navigation in the algorithmic multiverse. Further work includes study of natural computation by unconventional algorithms and constructive approaches.
Keywords: unconventional computing; computation beyond the Turing limit; axiomatic vs. constructive models; unconventional models of computation unconventional computing; computation beyond the Turing limit; axiomatic vs. constructive models; unconventional models of computation
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Dodig Crnkovic, G.; Burgin, M. Unconventional Algorithms: Complementarity of Axiomatics and Construction. Entropy 2012, 14, 2066-2080.

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