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A qualitative assessment of \(\alpha \)Rby in the perspective of the supervisory control theory

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Abstract

It becomes more and more evident today that SAT-solving approaches have the potential to verify properties and synthesize supervisors of controlled systems described with a high level of abstraction. Such approaches can be particularly appropriate when engineers give more importance to decentralized, hierarchical, and parameterized control paradigms than to centralized ones in the design of systems composed of multiple small agents. One advantage of declarative programming languages, such as relational logic, in specifying control problems, including their underlying properties and reasoning methods, is their proximity to the mathematical objects used in the formulation of the theory itself, which allows for implementing new fragments of it faster. The disadvantage is, however, that SAT-solving approaches do not lend themselves to efficient calculations of auxiliary objects involved in some control problems, even if they can be described with the logic at hand. In some cases, the latter is not sufficiently powerful to express the entire solution logically. Such difficulties can be circumvented with \(\alpha {\textsc {Rby}}\), a fusion of Alloy and Ruby. Based on earlier experiments conducted with Alloy, this paper provides a qualitative assessment of \(\alpha {\textsc {Rby}}\) and reports on the results of new experiments with two fragments of the supervisory control theory: state-based control and decentralized control.

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Notes

  1. https://github.com/maximerouthier/arby/.

  2. http://rstdenis.espaceweb.usherbrooke.ca/en/downloads/Alloy-models/ and http://rstdenis.espaceweb.usherbrooke.ca/en/downloads/aRby-programs/.

  3. The notation \(\delta (x, \sigma )!\) means that \(\delta (x, \sigma )\) is defined.

  4. The expression \(t \le s\) denotes that t is a prefix of s.

  5. \(\alpha {\textsc {Rby}}\) with SAT solver SAT4j was run on a 3.5 Ghz Intel Quad-Core i7 processor with 16GB of memory under Linux Ubuntu.

  6. An inaccuracy was discovered in [40]. The captions of Figs. 18 and 19 must be swapped.

  7. The symbol # denotes the size of a sequence s.

  8. DSML is the abbreviation for Domain-Specific Modeling Language.

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Authors and Affiliations

  1. Département d’informatique, Université de Sherbrooke, Sherbrooke, QC, J1K 2R1, Canada

    Maxime Routhier & Richard St-Denis

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  1. Maxime Routhier
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  2. Richard St-Denis
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Correspondence to Richard St-Denis.

Additional information

The authors would like to thank the Natural Sciences and Engineering Research Council of Canada (NSERC) for financial support. They are grateful to Aleksandar Milicevic for his prompt and valuable answers to numerous requests about \(\alpha {\textsc {Rby}}\). They would also like to thank the reviewers for their valuable comments and suggestions.

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Routhier, M., St-Denis, R. A qualitative assessment of \(\alpha \)Rby in the perspective of the supervisory control theory. Int J Softw Tools Technol Transfer 21, 121–141 (2019). https://doi.org/10.1007/s10009-017-0461-6

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