On Parameter Synthesis by Parallel Model Checking

Abstract

Abstract-An important problem in current computational systems biology is to analyse models of biological systems dynamics under parameter uncertainty. This paper presents a novel algorithm for parameter synthesis based on parallel model checking. The algorithm is conceptually universal with respect to the modelling approach employed. We introduce the algorithm, show its scalability, and examine its applicability on several biological models.

Parameter Identification and Model Ranking of Thomas Networks

“…We utilize the approach of colored model checking (CMC) as introduced in [2]. CMC takes a PKS S(R), a parametrization space P, and a Büchi automaton BA(ϕ).…”

“…CMC [2] is a heuristic method based on the idea that transitions within PKS are shared by many parametrizations, therefore utilizing a single PKS for a check (top-down) is significantly faster than doing a check on every single KS S(R, P).…”

“…Algorithm for colored model checking as presented in [2] does not specify, how distinct parametrizations should be stored and manipulated. For continuous models, we have used bounded intervals of values for each component, creating a parametrization space as a Cartesian product of those.…”

“…Our idea is based on the assumption that similar parametrizations generate similar KSs [2]. When computing a coloring of a PKS we split its parametrization space to …”

“…Barnat et al [2] introduced technique of colored LTL model checking (CMC) based on a heuristics reducing the computation effort by means of operating on the parametrization space in a top-down manner. In particular, maximal parametrization sets sharing a required behaviour are inferred instead of analyzing each possible parametrization individually.…”