Adaptive symbolic control for finite-state transition systems with grammatical inference

This note presents an approach that integrates elements from grammatical inference and game theory to address the problem of supervising finite-state transition systems operating in adversarial, partially known, rule-governed environments. The combined formulation produces controllers which guarantee that a transition system satisfies a task specification in the form of a logical formula, if and only 1) the true model of the environment is in the class of models inferable from positive data presentation (observations), 2) a characteristic sample of the environment's behavior is observed, and 3) the task specification is satisfiable given the capabilities described by the abstractions of the system and its environment.