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Model checking refers to the following problem: given a model of a system, test automatically whether this model meets a given specification.

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generic technique to build LTL/CTL formula that satisfy specific inputs to a model

I have an automaton, for example the below automaton and would like to generate a single formula (LTL or CTL, or some other representation) that satisfy exactly the traces provided. e.g., $t_1 = i^* …