In this paper, we propose a new automaton property of N-step nonblockingness for a given positive integer N. This property quantifies the standard nonblocking property by capturing the practical requirement that all tasks be completed within a bounded number of steps. Accordingly, we formulate a new N-step nonblocking supervisory control problem, and characterize its solvability in terms of a new concept of N-step language completability. It is proved that there exists a unique supremal N-step completable sublanguage of a given language, and we develop a generator-based algorithm to compute the supremal sublanguage. Finally, together with the supremal controllable sublanguage, we design an algorithm to compute a maximally permissive supervisory control solution to the new N-step nonblocking supervisory control problem.
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