Extremal combinatorics is the study of the size that a collection of objects must have in order to certainly satisfy a given property. Reaction systems are a recent formalism for computation inspired by chemical reactions. This work is a first contribution to the study of the behavior of large reaction systems by means of extremal combinatorics. We define several different properties that capture some basic and dynamical behaviors of a reaction system and we prove that they must necessarily be satisfied if the system is large enough. Explicit bounds and formulae are also provided.
Dennunzio, A., Formenti, E., Manzoni, L. (2015). Reaction systems and extremal combinatorics properties. THEORETICAL COMPUTER SCIENCE, 598, 138-149 [10.1016/j.tcs.2015.06.001].
Reaction systems and extremal combinatorics properties
DENNUNZIO, ALBERTO
;MANZONI, LUCA
2015
Abstract
Extremal combinatorics is the study of the size that a collection of objects must have in order to certainly satisfy a given property. Reaction systems are a recent formalism for computation inspired by chemical reactions. This work is a first contribution to the study of the behavior of large reaction systems by means of extremal combinatorics. We define several different properties that capture some basic and dynamical behaviors of a reaction system and we prove that they must necessarily be satisfied if the system is large enough. Explicit bounds and formulae are also provided.
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