Unconventional Algorithms: Complementarity of Axiomatics and Construction
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 flexibi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2012-10-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1099-4300/14/11/2066 |
| _version_ | 1828109203278921728 |
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| author | Gordana Dodig Crnkovic Mark Burgin |
| author_facet | Gordana Dodig Crnkovic Mark Burgin |
| author_sort | Gordana Dodig Crnkovic |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T10:58:59Z |
| format | Article |
| id | doaj.art-bba775047e4648f0b96c5cd140c1712b |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T10:58:59Z |
| publishDate | 2012-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-bba775047e4648f0b96c5cd140c1712b2022-12-22T04:28:41ZengMDPI AGEntropy1099-43002012-10-0114112066208010.3390/e14112066Unconventional Algorithms: Complementarity of Axiomatics and ConstructionGordana Dodig CrnkovicMark BurginIn 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.http://www.mdpi.com/1099-4300/14/11/2066unconventional computingcomputation beyond the Turing limitaxiomatic vs. constructive modelsunconventional models of computation |
| spellingShingle | Gordana Dodig Crnkovic Mark Burgin Unconventional Algorithms: Complementarity of Axiomatics and Construction Entropy unconventional computing computation beyond the Turing limit axiomatic vs. constructive models unconventional models of computation |
| title | Unconventional Algorithms: Complementarity of Axiomatics and Construction |
| title_full | Unconventional Algorithms: Complementarity of Axiomatics and Construction |
| title_fullStr | Unconventional Algorithms: Complementarity of Axiomatics and Construction |
| title_full_unstemmed | Unconventional Algorithms: Complementarity of Axiomatics and Construction |
| title_short | Unconventional Algorithms: Complementarity of Axiomatics and Construction |
| title_sort | unconventional algorithms complementarity of axiomatics and construction |
| topic | unconventional computing computation beyond the Turing limit axiomatic vs. constructive models unconventional models of computation |
| url | http://www.mdpi.com/1099-4300/14/11/2066 |
| work_keys_str_mv | AT gordanadodigcrnkovic unconventionalalgorithmscomplementarityofaxiomaticsandconstruction AT markburgin unconventionalalgorithmscomplementarityofaxiomaticsandconstruction |