The basis for this project consists in a mathematical framework previously developed by the applicant that allows to describe graph rewriting systems algebraically, the so-called rule algebraic framework. In order to advance and valorise the concept, this project proposes to develop a general concept for rule-algebraic simple rewriting (RaSiR), both for conventional graph rewriting and for a novel form of simplicial rewriting. Secondly, RaSiR will serve as the basis for developing rule-algebraic variants of trace compression and observable-update algorithms for the rewriting system Kappa. The final aim of the project consists in developing and implementing the so-called observable-centric bootstrapping algorithm (OCBA) as a module for the simulation suite KaSim for the Kappa language. Kappa is predominantly used for simulating biochemical reaction systems, which typically display an extremely high combinatorial complexity. The algorithms and software modules developed in this project will provide in particular an alternative to pure stochastic simulation via the SSA algorithm as currently implemented in KaSim, in the form of the OCBA module. This module will admit the generation of approximate observable distributions from individual pure states of the system by calculating algebraically truncations of the formal solution of the chemical master equation as well as the induced observable update functions. The project shall be hosted by Dr. Jean Krivine of the PPS team at IRIF at the University Paris-Diderot in France. Dr. Krivine is one of the two main developers of the KaSim simulation suite, and moreover one of the world experts in the theoretical and practical development of the programming language Kappa. IRIF will provide an ideal environment for the applicant to develop new skills, to be part the very interdisciplinary research team PPS, and to communicate and valorise the project results to the greater biochemical and systems biological simulation community.
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