"The RUBYX project will extend the theoretical foundations for the area of rule-based systems used in theoretical computer science to model biological and chemical processes with the aim of extending their areas of application to new areas. Rule-based systems give rise to systems of differential equations that describe the evolution of the biochemical systems modelled, but which are too complex to solve with current state-of-the art algorithms. RUBYX will address this shortcoming by (i) providing a theoretical characterisation of the intrinsic computational complexity of general rule-based systems; (ii) employ techniques from graph rewriting to investigate the optimality of existing techniques from Kappa calculus, and characterise the set of rule-based methods for which optimal methods exist; (iii) provide experimental in silico corroborationof the theoretical results. The RUBYX project aims to further strengthen the leading European position in the theoretical treatment of synthetic biology (the mathematical and computer scientific aspects of which have internationally leading experts in France, Italy and Scotland) by enabling a highly promising junior researcher in the area to interface with leading European experts in computational complexity theory and rewriting (with internationally leading experts in, amongst other countries, Denmark, Germany, and the Netherlands). The long-term strategic benefit to both the applicant and the European research area will be the (a) the establishment of further interaction between distinct areas of theoretical computer science, and (b) the extension and potential empirical verification of theoretical methods developed in Europe in areas of synthetic biology whose practical aspects are currently dominated by scientists in the United States."