A likelihood-ratio test for identifying probabilistic deterministic real-time automata from positive data

We adapt an algorithm (RTI) for identifying (learning) a deterministic real-time automaton (DRTA) to the setting of positive timed strings (or time-stamped event sequences). An DRTA can be seen as a deterministic finite state automaton (DFA) with time constraints. Because DRTAs model time using numbers, they can be exponentially more compact than equivalent DFA models that model time using states. We use a new likelihood-ratio statistical test for checking consistency in the RTI algorithm. The result is the RTI¿+ algorithm, which stands for real-time identification from positive data. RTI¿+ is an efficient algorithm for identifying DRTAs from positive data. We show using artificial data that RTI¿+ is capable of identifying sufficiently large DRTAs in order to identify real-world real-time systems