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Polynomial Equations over Finite, Discrete-Time Dynamical Systems

  • Alberto Dennunzio
  • Valentina Dorigatti
  • Enrico Formenti
  • Luca Manzoni
  • Antonio E. Porreca
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11115)

Abstract

We introduce an algebraic approach for the analysis and composition of finite, discrete-time dynamical systems based on the category-theoretical operations of product and sum (coproduct). This allows us to define a semiring structure over the set of dynamical systems (modulo isomorphism) and, consequently, to express many decomposition problems in terms of polynomial equations. We prove that these equations are, in general, algorithmically unsolvable, but we identify a solvable subclass. Finally, we describe an implementation of the semiring operations for the case of finite cellular automata.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Alberto Dennunzio
    • 1
  • Valentina Dorigatti
    • 1
  • Enrico Formenti
    • 2
  • Luca Manzoni
    • 1
  • Antonio E. Porreca
    • 1
  1. 1.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità degli Studi di Milano-BicoccaMilanItaly
  2. 2.Universite Côte d’Azur, CNRS, I3SSophia AntipolisFrance

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