Minimization of Finite State Automata Through Partition Aggregation

Abstract

We present a minimization algorithm for finite state automata that finds and merges bisimulation-equivalent states, identified through partition aggregation. We show the algorithm to be correct and run in time \( O \left( n^2 d^2 \left| \Sigma \right| \right) \), where n is the number of states of the input automaton \(M\), d is the maximal outdegree in the transition graph for any combination of state and input symbol, and \(\left| \Sigma \right| \) is the size of the input alphabet. The algorithm is slower than those based on partition refinement, but has the advantage that intermediate solutions are also language equivalent to \(M\). As a result, the algorithm can be interrupted or put on hold as needed, and the derived automaton is still useful. Furthermore, the algorithm essentially searches for the maximal model of a characteristic formula for \(M\), so many of the optimisation techniques used to gain efficiency in SAT solvers are likely to apply.