ϵ-Semantics computations on biological systems

Abstract

The assumption of being able to perform infinite precision measurements does not only lead to undecidability, but it also introduces artifacts in the mathematical models that do not correspond to observable behaviours of systems under study. When bounded spatial regions are involved, such issues can be avoided if arbitrarily small sets of points are not definable in the mathematical setting. -semantics were introduced in this spirit. In this paper we investigate the use of -semantics deeper, in the context of reachability analysis of hybrid automata. In particular, we focus on two -semantics and reason about their computability. We then try our approach on biological model analysis to give evidence about the effectiveness of the methodology.

Parameter synthesis of polynomial dynamical systems

“…Recently several methods and tools have been developed for reachability analysis and parameter synthesis. Some examples are HyTech [41], d/dt [6], Breach [24], SpaceEx [35], Ariadne [10], Flow* [17], pyHybridAnalysis [15,16], dReach [52], CORA [3], DynIbex [57], JuliaReach [11], Kaa [51], and HyPro [64].…”