Abstract
We introduce and study a new class of automata able to consume and produce multisets; we call them Mealy multiset automata. We are interested in their algebraic and coalgebraic properties. After some useful properties of multisets, we present the notions of bisimulation, observability, and behavior for Mealy multiset automata. We give a characterization of the bisimulation between two Mealy multiset automata, and a result relating their general behavior to their sequential behavior. We describe an endofunctor of the category of Set such that a Mealy multiset automaton is a coalgebra of this functor. This functor preserves coproducts, coequalizers, and weak pullbacks. Moreover, the new defined bisimulation is an instance of a more general coalgebraic definition.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Aczel, P., Mendler, N.: Category Theory and Computer Science. LNCS, vol. 389, pp. 357–365. Springer, Berlin (1989)
Barr, M., Wells, C.: Category Theory Lecture Notes for ESSLLI, Available on-line at http://www.let.uu.nl/esslli/Courses/barr/barrwells.ps
Ciobanu, G., Gontineac, M.: Mealy membrane automata and P systems complexity. In: Gutiérrez-Naranjo, M.A., Păun, G., Pérez-Jiménez, M.J. (eds.) ESF Workshop, pp. 149–164. Fenix Editora, Sevilla (2005)
Ciobanu, G., Gontineac, M.: Mealy multiset automata. International Journal of Foundations of Computer Science (to appear) (2006)
Csuhaj-Varju, E., Martin-Vide, C., Mitrana, V.: Multiset automata. In: Calude, C.S., Pun, G., Rozenberg, G., Salomaa, A. (eds.) Multiset Processing. LNCS, vol. 2235, pp. 69–83. Springer, Heidelberg (2001)
Ehresmann, A.C., Vanbremersch, J.-P.: Hierarchical evolutive systems: A mathematical model for complex systems. Bull. of Math. Biol. 49, 13–50 (1987)
Eilenberg, S.: Automata. Languages and Machines, vol. A. Academic Press, London (1976)
Eilenberg, S., MacLane, S.: The general theory of natural equivalences. Trans. Amer. Math. Soc. 58, 231–294 (1945)
Fisher, M.J., Malcolm, G., Paton, R.C.: Spatio-logical processes in intracellular signalling. Biosystems 55, 83–92 (2000)
Kuich, W., Salomaa, A.: Semirings, Automata, Languages. Springer, Berlin (1986)
Păun, G.: Membrane Computing. An Introduction. Springer, Berlin (2002)
Rutten, J.: Universal coalgebra: a theory of systems. Theoretical Computer Science 249, 3–80 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ciobanu, G., Gontineac, V.M. (2006). Algebraic and Coalgebraic Aspects of Membrane Computing. In: Freund, R., Păun, G., Rozenberg, G., Salomaa, A. (eds) Membrane Computing. WMC 2005. Lecture Notes in Computer Science, vol 3850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11603047_13
Download citation
DOI: https://doi.org/10.1007/11603047_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30948-2
Online ISBN: 978-3-540-32340-2
eBook Packages: Computer ScienceComputer Science (R0)