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A central computational problem in the realm of automata theory is the problem of determining whether a finite automaton A has a synchronizing word. This problem has found applications in a variety of subfields of artificial intelligence, including planning, robotics, and multi-agent systems. In this work, we study this problem within the framework of diversity of solutions, an up-and-coming trend in the field of artificial intelligence where the goal is to compute a set of solutions that are sufficiently distinct from one another. We define a notion of diversity of solutions that is suitable for contexts were solutions are strings that may have distinct lengths. Using our notion of diversity, we show that for each fixed r ∈ N, each fixed finite automaton A, and each finite automaton B given at the input, the problem of determining the existence of a diverse set {w1,w2, . . . ,wr} ⊆ L(B) of words that are synchronizing for A can be solved in polynomial time. Finally, we generalize this result to the realm of conformant planning, where the goal is to devise plans that achieve a goal irrespectively of initial conditions and of nondeterminism that may occur during their execution.
Multiagent Systems, Coordination and Cooperation, Multiagent Planning, Synchronization, Conformant Planning
Multiagent Systems, Coordination and Cooperation, Multiagent Planning, Synchronization, Conformant Planning
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