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A verified algorithm enumerating event structures

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Bowles_2017_A_verified_algorithm_CICM2017_AAM.pdf (341.9Kb)
Date
2017
Author
Bowles, Juliana Kuster Filipe
Caminati, Marco Bright
Keywords
QA75 Electronic computers. Computer science
QA76 Computer software
DAS
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Abstract
An event structure is a mathematical abstraction modeling concepts as causality, conflict and concurrency between events. While many other mathematical structures, including groups, topological spaces, rings, abound with algorithms and formulas to generate, enumerate and count particular sets of their members, no algorithm or formulas are known to generate or count all the possible event structures over af inite set of events. We present an algorithm to generate such a family, along with a functional implementation verified using Isabelle/HOL. As byproducts, we obtain a verified enumeration of all possible preorders and partial orders. While the integer sequences counting preorders and partial orders are already listed on OEIS (On-line Encyclopedia of Integer Sequences), the one counting event structures is not. We therefore used our algorithm to submit a formally verified addition, which has been successfully reviewed and is now part of the OEIS.
Citation
Bowles , J K F & Caminati , M B 2017 , A verified algorithm enumerating event structures . in H Geuvers , M England , O Hasan , F Rabe & O Teschke (eds) , Intelligent Computer Mathematics : 10th International Conference, CICM 2017, Edinburgh, UK, July 17-21, 2017, Proceedings . Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence) , vol. 10383 , Springer , Cham , pp. 239-254 , 10th Conference on Intelligent Computer Mathematics (CICM 2017) , Edinburgh , United Kingdom , 17/07/17 . https://doi.org/10.1007/978-3-319-62075-6_17
 
conference
 
Publication
Intelligent Computer Mathematics
DOI
https://doi.org/10.1007/978-3-319-62075-6_17
ISSN
0302-9743
Type
Conference item
Rights
© 2017, Springer. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at link.springer.com / https://doi.org/10.1007/978-3-319-62075-6_17
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/11248

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