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In a distributed system, detecting whether a given logical predicate is true on the global states is fundamental for testing and debugging the program. Detecting predicates by examining all global states is intractable due to the combinatorial nature of the problem. This work designs an efficient online algorithm that identifies the consistent and useless states each time a new state is reported. This paper formulates the optimality of detecting algorithms in terms of pseudo states, which are employed to represent unknown states to the monitor process. Based on this technique, memory space of the debugger can be minimized by removing the useless states without affecting the debugging results. While minimizing memory space, the proposed algorithm requires only O( p 2 M) time in total, where p is the number of processes, and M is the number of reported states.

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