Goal-Oriented Reduction of Automata Networks

We consider networks of finite-state machines having local transitions conditioned by the current state of other automata. In this paper, we introduce a reduction procedure tailored for reachability properties of the form “from global state s, there exists a sequence of transitions leading to a state where an automaton g is in a local state ⊤”. By analysing the causality of transitions within the individual automata, the reduction identifies local transitions which can be removed while preserving all the minimal traces satisfying the reachability property. The complexity of the procedure is polynomial with the total number of local transitions, and exponential with the maximal number of local states within an automaton. Applied to Boolean and multi-valued networks modelling dynamics of biological systems, the reduction can shrink down significantly the reachable state space, enhancing the tractability of the model-checking of large networks.