Incremental determinization of finite automata in model-based diagnosis of active systems

Abstract

Generating a deterministic finite automaton (DFA) equivalent to a nondeterministic one (NFA) is traditionally accomplished by subset-construction (SC). This is the right choice in case a single transformation is needed. If, instead, the NFA is repeatedly extended, one transition each time, and the DFA corresponding to each extension is needed in real-time, SC is bound to poor performances. In order to cope with these difficulties, an algorithm called incremental subset-construction (ISC) is proposed, which makes up the new DFA as an extension of the previous DFA, avoiding to start from scratch each time, thereby pursuing computational reuse. Although conceived within the application domain of model-based diagnosis of active systems, the algorithm is general in nature, hence it can be exploited for incremental determinization of any NFA. Massive experimentation indicates that, while comparable in space complexity, incremental determinization of finite automata is, in time, far more efficient than traditional determinization by SC. © 2008 Springer-Verlag Berlin Heidelberg.