A Likelihood-Ratio Test for Identifying Probabilistic Deterministic Real-Time Automata from Positive Data

Abstract

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.