Abstract. Conformance testing for finite state machines and regular inference both aim at identifying the model structure underlying a black box system on the basis of a limited set of observations. Whereas the former technique checks for equivalence with a given conjecture model, the latter techniques addresses the corresponding synthesis problem by means of techniques adopted from automata learning. In this paper we establish a common framework to investigate the similarities of these techniques by showing how results in one area can be transferred to results in the other and to explain the reasons for their differences.

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In regular inference, the problem is to infer a regular language, typically represented by a deterministic finite automaton (DFA) from answers to a finite set of membership queries, each of which asks whether the language contains a certain word. There are many algorithms for learning DFAs, the most well-known being the Ä £ algorithm due to Dana Angluin.However, there are almost no extensions of these algorithms to the setting of timed systems. We present an algorithm for inferring a model of a timed system using Angluin's setup. One of the most popular model for timed system is timed automata. Since timed automata can freely use an arbitrary number of clocks, we restrict our attention to systems that can be described by event-recording automata (DERAs). In previous work, we have presented an algorithm for inferring a DERA in the form of a region graph. In this paper, we present a novel inference algorithm for DERAs, which avoids constructing a (usually prohibitively large) region graph. We must then develop techniques for inferring guards on transitions of a DERA. Our construction deviates from previous work on inference of DERAs in that it first constructs a so called timed decision tree from observations of system behavior, which is thereafter folded into an automaton.

In regular inference, a regular language is inferred from answers to a finite set of membership queries, each of which asks whether the language contains a certain word. One of the most well-known regular inference algorithms is the L * algorithm due to Dana Angluin. However, there are almost no extensions of these algorithms to the setting of timed systems. We extend Angluin's algorithm for on-line learning of regular languages to the setting of timed systems. Since timed automata can freely use an arbitrary number of clocks, we restrict our attention to systems that can be described by deterministic event-recording automata (DERAs). We present three algorithms, TL * sg , TL * nsg and TL * s , for inference of DERAs. In TL * sg and TL * nsg , we further restrict event-recording automata to be event-deterministic in the sense that each state has at most one outgoing transition per action; learning such an automaton becomes significantly more tractable. The algorithm TL * nsg builds on TL * sg , by attempts to construct a smaller (in number of locations) automaton. Finally, TL * s is a learning algorithm for a full class of deterministic event-recording automata, which infers a so called simple DERA, which is similar in spirit to the region graph.