Technical communique: String execution time for finite languages: Max is easy, min is hard

Authors:
Rong Su;Gerhard Woeginger
Affiliations:
Division of Control and Instrumentation, School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore;Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
Venue:
Automatica (Journal of IFAC)
Year:
2011

Citing 3
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Abstract

In performance evaluation or supervisory control, we often encounter problems of determining the maximum or minimum string execution time for a finite language when estimating the worst-case or best-case performance. It has been shown in the literature that the time complexity for computing the maximum string execution time for a finite language is polynomial with respect to the size of an automaton recognizer of that language and the dimension of the corresponding resource matrices. In this paper we provide a more efficient algorithm to compute such maximum string execution time. Then we show that it is NP-complete to determine the minimum string execution time.