Synchronizing automata over nested words

We extend the concept of a synchronizing word from deterministic finite-state automata (DFA) to nested word automata (NWA): A well-matched nested word is called synchronizing if it resets the control state of any configuration, i. e., takes the NWA from all control states to a single control state. We show that although the shortest synchronizing word for an NWA, if it exists, can be (at most) exponential in the size of the NWA, the existence of such a word can still be decided in polynomial time. As our main contribution, we show that deciding the existence of a short synchronizing word (of at most given length) becomes PSPACE-complete (as opposed to NP-complete for DFA). The upper bound makes a connection to pebble games and Strahler numbers, and the lower bound goes via small-cost synchronizing words for DFA, an intermediate problem that we also show PSPACE-complete. We also characterize the complexity of a number of related problems, using the observation that the intersection nonemptiness problem for NWA is EXP-complete

Computation of synchronizing sequences for a class of 1-place-unbounded synchronized Petri nets

Identification of a final state after red a test is one of the fundamental testing problems for discrete event systems and synchronizing sequences represents a conventional solution to this problem. In this paper, we consider systems modeled by a special class of synchronized Petri nets, called 1-place-unbounded, that contain a single unbounded place. The infinite reachability spaces of such nets can be characterized by two types of finite graphs, called improved modified coverability graph and weighted automata with safety conditions. In case these two finite graphs are deterministic, we develop novel computation algorithms for synchronizing sequences for this class of nets by decomposing the finite graphs into strongly connected components

Computation of synchronizing sequences for a class of 1-place-unbounded synchronized Petri nets

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