Discrete Event Dynamic Systems
, Volume 15, Issue 2, pp 145167
PSPACEcompleteness of Modular Supervisory Control Problems*
 Kurt RohloffAffiliated withDepartment of Electrical Engineering and Computer Science, The University of Michigan
 , Stéphane LafortuneAffiliated withDepartment of Electrical Engineering and Computer Science, The University of Michigan Email author
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In this paper we investigate computational issues associated with the supervision of concurrent processes modeled as modular discreteevent systems. Here, modular discreteevent systems are sets of deterministic finitestate automata whose interaction is modeled by the parallel composition operation. Even with such a simple model process model, we show that in general many problems related to the supervision of these systems are PSPACEcomplete. This shows that although there may be spaceefficient methods for avoiding the stateexplosion problem inherent to concurrent processes, there are most likely no timeefficient solutions that would aid in the study of such “largescale” systems. We show our results using a reduction from a special class of automata intersection problem introduced here where behavior is assumed to be prefixclosed. We find that deciding if there exists a supervisor for a modular system to achieve a global specification is PSPACEcomplete. We also show many verification problems for system supervision are PSPACEcomplete, even for prefixclosed cases. Supervisor admissibility and online supervision operations are also discussed.
Keywords
modular systems supervisory control verification computational complexity Title
 PSPACEcompleteness of Modular Supervisory Control Problems*
 Journal

Discrete Event Dynamic Systems
Volume 15, Issue 2 , pp 145167
 Cover Date
 200506
 DOI
 10.1007/s1062600462105
 Print ISSN
 09246703
 Online ISSN
 15737594
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 modular systems
 supervisory control
 verification
 computational complexity
 Industry Sectors
 Authors

 Kurt Rohloff ^{(1)}
 Stéphane Lafortune ^{(1)}
 Author Affiliations

 1. Department of Electrical Engineering and Computer Science, The University of Michigan, 1301 Beal Ave., Ann Arbor, MI, 481092122, USA