A New Sandpile Model with Smoothness Assumptions

Issue title: Reachability Problems for Infinite State Systems

Guest editors: Parosh Aziz Abdulla, Stéphane Demri, Alain Finkel, Jérôme Leroux and Igor Potapov

Article type: Research Article

Authors: Brocchi, Stefano^{a; *; †} | Massazza, Paolo^{b; †}

Affiliations: [a] Università degli Studi di Firenze, Dipartimento di Matematica e Informatica ‘U. Dini’, Viale G. B. Morgagni 65, 50134 Florence, Italy. stefano.brocchi@unifi.it | [b] Università degli Studi dell’Insubria, Dipartimento di Scienze Teoriche e Applicate, Via Mazzini 5, 21100 Varese, Italy. paolo.massazza@uninsubria.it

Correspondence: [*] Address for correspondence: Università degli Studi di Firenze, Dipartimento di Matematica e Informatica ‘U. Dini’, Viale G. B. Morgagni 65, 50134 Florence, Italy

Note: [†] Partially supported by project M.I.U.R. PRIN 2010-2011: Automi e linguaggi formali: aspetti matematici e applicativi

Abstract: We consider two new granular dynamical systems obtained from the Sand Pile Model SPM(n) by adding a smoothness condition. First, we define the Smooth Sand Pile Model SmSPM(n) and we provide a characterization of the reachable states, together with some interesting properties of the resulting lattice. Then we extend it to SmSPM*(n), a related dynamical system with a more complex lattice structure.

Keywords: sand piles, discrete dynamical system

DOI: 10.3233/FI-2016-1314

Journal: Fundamenta Informaticae, vol. 143, no. 3-4, pp. 261-286, 2016