Selected Applications of Semirings

Kazimierz Głazek
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Kazimierz Głazek: University of Zielona Góra, Institute of Mathematics

Chapter 5 in A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences, 2002, pp 67-87 from Springer

Abstract: Abstract There are numerous applications of semirings in various branches of mathematics and computer science. We have already mentioned many applications in previous sections. The reader will find papers which use semirings in almost all sections of Mathematical Reviews or Zentralblatt für Mathematik (although unfortunately the terminology is not standard). For example, there are some applications of semirings to modelling of economies (see, e.g., R.P. Gilles, H. Haller & P.H.M. Ruys [1994]), queueing theory (see, e.g., F.L. Baccelli & P. Brémaud [1994], F.L. Baccelli & D. Hong [2000], F.L. Baccelli & V. Schmidt [1996], N.K. Krivulin [1995], and J.-Y. Le Boudec & P. Thiran [2001]), social networks analysis (see, e.g., V. Batagelj [1994]), consensus theory (see the book by K.-H. Kim, F.W. Roush [1980a]), modern control theory of psychological phenomena (see, e.g., Z.-Q. Cao [1982a], [1982b]), computations of biopolymers (see, e.g., A.V. Finkelstein & M.A. Roytberg [1993], DNA computations (see, e.g., A. Mateescu [1998]), mathematical morphology in the sense of J. Serra [1982] (see, e.g., Ch. Ronse & H.J.A.M. Heijmans [1998]), and penalty theory in artificial intelligence (see, e.g., F. Dupin de Saint-Cyr, J. Lang & T. Schiex [1994]). Semirings are used for a physical theory on cognitive processes; see, e.g., D. Gernert [2000].

Keywords: Formal Power Series; Finite Automaton; Discrete Event System; Automaton Theory; Triangular Norm (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-94-015-9964-1_6

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