Grammars for Discrete Dynamics

The paper reviews a new perspective to discover and compute discrete dynamics, which is based on MP grammars. They are a particular type of multiset rewriting grammars, introduced in 2004 for modeling metabolic systems, which express dynamics in terms of finite difference equations. MP regression algorithms, providing the best MP grammar reproducing a given time series of observed states, were introduced since 2008. Applications of these grammars to the analysis of biological dynamics were developed, and their flexibility to model complex and uncertain phenomena was apparent in the last years. In this paper we recall the main features of this modeling framework, by stressing their peculiarity to afford complex situations, where classical continuous methods cannot be applied or are computationally prohibitive. Moreover, the computational universality of MP grammars of a very simple type is shown, and one of the most relevant cases of MP biological models is shortly presented.