{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T17:57:05Z","timestamp":1754157425794,"version":"3.41.2"},"reference-count":14,"publisher":"Emerald","issue":"9","license":[{"start":{"date-parts":[[2009,10,16]],"date-time":"2009-10-16T00:00:00Z","timestamp":1255651200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009,10,16]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-heading\">Purpose<\/jats:title><jats:p>The purpose of this paper is to fill a gap between experimental and abstract\u2010theoretic models of reaction\u2010diffusion computing. Chemical reaction\u2010diffusion computers are amongst leading experimental prototypes in the field of unconventional and nature\u2010inspired computing. In the reaction\u2010diffusion computers, the data are represented by concentration profiles of reagents, information is transferred by propagating diffusive and phase waves, computation is implemented in interaction of the traveling patterns, and results of the computation are recorded as a final concentration profile.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title><jats:p>The paper analyzes a possibility of co\u2010algebraic representation of the computation in reaction\u2010diffusion systems using reaction\u2010diffusion cellular\u2010automata models.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>Using notions of space\u2010time trajectories of local domains of a reaction\u2010diffusion medium the logic of trajectories is built, where well\u2010formed formulas and their truth\u2010values are defined by co\u2010induction. These formulas are non\u2010well\u2010founded set\u2010theoretic objects. It is demonstrated that the logic of trajectories is a co\u2010algebra.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Research limitations\/implications<\/jats:title><jats:p>The paper uses the logic defined to establish a semantical model of the computation in reaction\u2010diffusion media.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>The work presents the first ever attempt toward mathematical formalization of reaction\u2010diffusion processes and is built building up semantics of reaction\u2010diffusion computing. It is envisaged that the formalism produced will be used in developing programming techniques of reaction\u2010diffusion chemical media.<\/jats:p><\/jats:sec>","DOI":"10.1108\/03684920910991504","type":"journal-article","created":{"date-parts":[[2009,10,17]],"date-time":"2009-10-17T07:04:03Z","timestamp":1255763043000},"page":"1518-1531","source":"Crossref","is-referenced-by-count":12,"title":["Toward semantical model of reaction\u2010diffusion computing"],"prefix":"10.1108","volume":"38","author":[{"given":"Andrew","family":"Schumann","sequence":"first","affiliation":[]},{"given":"Andrew","family":"Adamatzky","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"key":"key2022020520421121800_b1","unstructured":"Adamatzky, A. (1994), \u201cReaction\u2010diffusion algorithm for constructing discrete generalized Voronoi diagram\u201d, Neural Network World, Vol. 6, pp. 635\u201043."},{"key":"key2022020520421121800_b2","doi-asserted-by":"crossref","unstructured":"Adamatzky, A. (2001), Computing in Nonlinear Media and Automata Collectives, Institute of Physics Publishing, London.","DOI":"10.1201\/9781420034547"},{"key":"key2022020520421121800_b5","doi-asserted-by":"crossref","unstructured":"Adamatzky, A. and Wuensche, A. (2007), \u201cComputing in spiral rule reaction\u2010diffusion hexagonal cellular automaton\u201d, Complex Systems, Vol. 16, p. 4.","DOI":"10.25088\/ComplexSystems.16.4.277"},{"key":"key2022020520421121800_b3","unstructured":"Adamatzky, A., de Lacy Costello, B. and Asai, T. (2005), Reaction\u2010Diffusion Computers, Elsevier, Amsterdam."},{"key":"key2022020520421121800_b4","doi-asserted-by":"crossref","unstructured":"Adamatzky, A., Wuensche, A. and de Lacy Costello, B. 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(2007), \u201cp\u2010Adic multiple\u2010validity and p\u2010Adic valued logical calculi\u201d, Journal of Multiple\u2010Valued Logic and Soft Computing, Vol. 13 Nos 1\/2, pp. 29\u201060."},{"key":"key2022020520421121800_b13","doi-asserted-by":"crossref","unstructured":"Schumann, A. (2008), \u201cNon\u2010archimedean fuzzy and probability logic\u201d, Journal of Applied Non\u2010Classical Logics, Vol. 1.","DOI":"10.3166\/jancl.18.29-48"},{"key":"key2022020520421121800_b14","doi-asserted-by":"crossref","unstructured":"Wuensche, A. and Adamatzky, A. (2006), \u201cOn spiral glider\u2010guns in hexagonal cellular automata: activator\u2010inhibitor paradigm\u201d, Int. J. 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