Independent Dynamics Hybrid Automata in System Biology


Independent Dynamics Hybrid Automata (IDA) describe a new class of hybrid automata that extends decidable O-minimal automata by further allowing identity resets. We define the conditions under which reachability is decidable over IDA. These conditions involve the satisfiability of first-order formulæ that limit the interval of time we need to consider to study reachability. In order to prove the decidability of reachability we mainly exploit the decidability of the first-order formulæ which define IDA. IDA are useful in the modeling of biological systems where it is possible to have variables which continue their flows independently (e.g., external input reactants). We briefly comment on how to model bacterial chemotaxis using IDA.

Algebraic Biology – Computer Algebra in Biology