KAT + B!

Abstract

It is known that certain program transformations require a small amount of mutable state, a feature not explicitly provided by Kleene algebra with tests (KAT). In this paper we show how to axiomatically extend KAT with this extra feature in the form of mutable tests. The extension is conservative and is formulated as a general commutative coproduct construction. We give several results on deductive completeness and complexity of the system, as well as some examples of its use.

@inproceedings{GKM14,
  author = {Niels Bj{\o}rn Bugge Grathwohl, Dexter Kozen, and Konstantinos Mamouras},
  title = {KAT + B!},
  booktitle = {Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)},
  series = {CSL-LICS '14},
  isbn = {978-1-4503-2886-9},
  location = {Vienna, Austria},
  pages = {44:1--44:10},
  articleno = {44},
  numpages = {10},
  url = {http://doi.acm.org/10.1145/2603088.2603095},
  doi = {10.1145/2603088.2603095},
  publisher = {ACM},
  address = {New York, NY, USA},
  keywords = {Kleene algebra, Kleene algebra with tests, verification},
  year = {2014},
  abstract = {It is known that certain program transformations require a small
              amount of mutable state, a feature not explicitly provided by Kleene
              algebra with tests (KAT). In this paper we show how to axiomatically
              extend KAT with this extra feature in the form of mutable tests. The
              extension is conservative and is formulated as a general commutative
              coproduct construction. We give several results on deductive
              completeness and complexity of the system, as well as some examples of
              its use.},
}