We present an algorithm for active learning of deterministic timed automata with multiple clocks. The algorithm is within the querying framework of Angluin's $L^*$ algorithm and follows the idea proposed in existing work on the active learning of deterministic one-clock timed automata. We introduce an equivalence relation over the reset-clocked language of a timed automaton and then transform the learning problem into learning the corresponding reset-clocked language of the target automaton. Since a reset-clocked language includes the clock reset information which is not observable, we first present the approach of learning from a powerful teacher who can provide reset information by answering reset information queries from the learner. Then we extend the algorithm in a normal teacher situation in which the learner can only ask standard membership query and equivalence query while the learner guesses the reset information. We prove that the learning algorithm terminates and returns a correct deterministic timed automaton. Due to the need of guessing whether the clocks reset at the transitions, the algorithm is of exponential complexity in the size of the target automaton.

中文翻译：

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学习确定性多时钟定时自动机

我们提出了一种用于主动学习具有多个时钟的确定性时间自动机的算法。该算法位于 Angluin 的 $L^*$ 算法的查询框架内，并遵循现有确定性单时钟定时自动机主动学习工作中提出的思想。我们在定时自动机的重置时钟语言上引入等价关系，然后将学习问题转化为学习目标自动机相应的重置时钟语言。由于重置时钟语言包含不可观察的时钟重置信息，因此我们首先提出向强大的教师学习的方法，该教师可以通过回答学习者的重置信息查询来提供重置信息。然后，我们将算法扩展到正常的教师情况，其中学习者只能提出标准隶属度查询和等价查询，而学习者则猜测重置信息。我们证明学习算法终止并返回正确的确定性定时自动机。由于需要猜测时钟是否在转换时重置，该算法的复杂度随着目标自动机的大小而呈指数级增长。