Abstract
AbstractConcurrent Kleene Algebra (CKA) extends basic Kleene algebra with a parallel composition operator, which enables reasoning about concurrent programs. However, CKA fundamentally misses tests, which are needed to model standard programming constructs such as conditionals and $$\mathsf {while}$$
while
-loops. It turns out that integrating tests in CKA is subtle, due to their interaction with parallelism. In this paper we provide a solution in the form of Concurrent Kleene Algebra with Observations (CKAO). Our main contribution is a completeness theorem for CKAO. Our result resorts on a more general study of CKA “with hypotheses”, of which CKAO turns out to be an instance: this analysis is of independent interest, as it can be applied to extensions of CKA other than CKAO.
Publisher
Springer International Publishing
Reference29 articles.
1. Anderson, C.J., Foster, N., Guha, A., Jeannin, J.B., Kozen, D., Schlesinger, C., Walker, D.: NetKAT: Semantic foundations for networks. In: POPL. pp. 113–126. ACM (2014)
2. Birkhoff, G., Bartee, T.C.: Modern applied algebra. McGraw-Hill (1970)
3. Bonchi, F., Pous, D.: Checking NFA equivalence with bisimulations up to congruence. In: POPL. pp. 457–468 (2013)
4. Brunet, P., Pous, D., Struth, G.: On decidability of concurrent Kleene algebra. In: CONCUR. pp. 28:1–28:15 (2017)
5. Cohen, E.: Hypotheses in Kleene algebra. Tech. rep., Bellcore (1994)
Cited by
8 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. An Algebraic Language for Specifying Quantum Networks;Proceedings of the ACM on Programming Languages;2024-06-20
2. On Tools for Completeness of Kleene Algebra with Hypotheses;Logical Methods in Computer Science;2024-05-16
3. A Complete Inference System for Skip-free Guarded Kleene Algebra with Tests;Programming Languages and Systems;2023
4. Axiomatizing recursion-free, regular monitors;Journal of Logical and Algebraic Methods in Programming;2022-06
5. Concurrent NetKAT;Programming Languages and Systems;2022