Decidable First-Order Transition Logics for PA-Processes

We show decidability of several first-order logics based upon the reachability predicate in PA. The main tool we use is the recognizability by tree automata of the reachability relation between PA-processes. This approach and the transition logics we use allow a smooth and general treatment of parameterized model checking for PA. Then the logic is extended to handle a general notion of costs of PA-steps. In particular, when costs are Parikh images of traces, we show decidability of a transition logic extended by some form of first-order reasoning over costs.

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