Concurrent Kleene Algebra with Observations: from Hypotheses to Completeness

02/22/2020
by   Tobias Kappé, et al.
0

Concurrent 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 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
11/16/2018

Kleene Algebra with Observations

Kleene algebra with tests (KAT) is an algebraic framework for reasoning ...
research
10/24/2022

On Tools for Completeness of Kleene Algebra with Hypotheses

In the literature on Kleene algebra, a number of variants have been prop...
research
06/08/2019

Algebra of Concurrent Games

We introduce parallelism into the basic algebra of games to model concur...
research
07/15/2020

Partially Observable Concurrent Kleene Algebra

We introduce partially observable concurrent Kleene algebra (POCKA), an ...
research
05/04/2018

Encoding fairness in a synchronous concurrent program algebra: extended version with proofs

Concurrent program refinement algebra provides a suitable basis for supp...
research
10/31/2019

Pomsets with Boxes: Protection, Separation, and Locality in Concurrent Kleene Algebra

Concurrent Kleene Algebra is an elegant tool for equational reasoning ab...
research
05/17/2022

Local Completeness Logic on Kleene Algebra with Tests

Local Completeness Logic (LCL) has been put forward as a program logic f...

Please sign up or login with your details

Forgot password? Click here to reset