Formal Correctness of Result Checking for Priority Queues

We formally prove the correctness of the time super-e cient result checker for priority queues, which is implemented in LEDA [17]. A priority queue is a data structure that supports insertion, deletion and retrieval of the minimal element, relative to some order. A result checker for priority queues is a data structure that monitors the input and output of the priority queue. Whenever the user requests a minimal element, it checks that the returned element is indeed minimal. In order to do this, the checker makes use of a system of lower bounds. We have veri ed that, for every execution sequence in which the checker accepts the outputs, the priority queue returned the correct minimal elements. For the formal veri cation, we used the rst-order theorem prover Saturate [25].