Incremental Determinization and Minimization of Finite Acyclic Automata

The determinization of a nondeterministic finite automaton (NFA) N is the process of generating a deterministic finite automaton (DFA) D equivalent to (sharing the same regular language of) N. The minimization of D is the process of generating the minimal DFA M equivalent to D. Classical algorithms for determinization and minimization are available in the literature for several decades. However, they operate monolithically, assuming that the finite automaton to be either determinized or minimized is given once and for all. By contrast, we consider determinization and minimization in a dynamic context, where N expands over time: after each expansion, determinization and minimization of N into M is required. Using classical monolithic algorithms to solve this problem is bound to poor performances. An algorithm for incremental determinization and minimization of acyclic finite automata, called IDMA, is proposed. Despite being conceived within the narrow domain of model-based diagnosis and monitoring of active systems, the algorithm is general-purpose in nature. Experimental evidence indicates that IDMA is far more efficient than classical algorithms in solving incremental determinization and minimization problems.