A relational view of recurrence and attractors in state transition dynamics

Authors:
Giuseppe Scollo;Giuditta Franco;Vincenzo Manca
Affiliations:
Department of Mathematics and Computer Science, University of Catania, Catania, Italy;Department of Computer Science, University of Verona, Verona, Italy;Department of Computer Science, University of Verona, Verona, Italy
Venue:
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
Year:
2006

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Abstract

The classical dynamics concepts of recurrence and attractor are analysed in the basic mathematical setting of state transition systems, where both time and space are discrete, and no structure is assumed on the state space besides a binary transition relation. This framework proves useful to the dynamical analysis of computations and biomolecular processes. Here a relational formulation of this framework is presented, where the concepts of attractor and recurrence surface in two variants, respectively relating to the two fundamental modalities. A strong link between recurrence and both existence and extent of attractors, in either variant, is established by a novel characterization theorem.