Reaction systems with duration

  • Authors:

  • Robert Brijder;Andrzej Ehrenfeucht;Grzegorz Rozenberg

  • Affiliations:

  • Leiden Institute of Advanced Computer Science, Leiden Center for Natural Computing, Leiden University, The Netherlands;Department of Computer Science, University of Colorado at Boulder;Leiden Institute of Advanced Computer Science, Leiden University, The Netherlands and Department of Computer Science, University of Colorado at Boulder

  • Venue:
  • Computation, cooperation, and life
  • Year:
  • 2011

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Abstract

A reaction system is essentially a finite set of reactions, where each reaction consists of a finite set of reactants (needed for the reaction to take place), a finite set of inhibitors (each of which inhibits the reaction from taking place), and a finite set of products produced when the reaction takes place. A crucial feature of a reaction system is that (unless introduced from outside the system) an element (entity) from a current state will belong also to the successor state only if it is in the product set of a reaction that took place in the current state. In other words, an entity vanishes unless it is sustained by a reaction -- a sort of "immediate decay" property. In this paper we relax this property, by providing each entity x with its duration d(x), which guarantees that x will last through at least d(x) consecutive states. Such reaction systems with duration are investigated in this paper. Among others we demonstrate that duration/decay is a result of an interaction with a "structured environment", and we also investigate fundamental properties of state sequences of reaction systems with duration.