Models of Concurrent Kleene Algebra

Abstract

Kleene Algebra and variants thereof have been successfully used in verification of se- quential programs. The leap to concurrent programs offers many challenges, both in terms of devising the right foundations to study concurrent variants of Kleene Algebra but also in finding the right models to enable effective verification of relevant programs. In this talk, we will review existing and ongoing work on concurrent Kleene Algebra with a focus on a variant called partially observable concurrent Kleene algebra (POCKA). POCKA offers an algebraic framework to reason about concurrent programs with control structures, such as conditionals and loops. We will show how a previously developed technique for com- pleteness of Kleene Algebra can be lifted to prove that POCKA is a sound and complete axiomatization of a model of partial observations. We illustrate the use of the framework in the analysis of sequential consistency, i.e., whether programs behave as if memory accesses taking place were interleaved and executed sequentially.The work described in this invited talk is based on [1, 2, 3], and it is joint with a won- derful group of people: Paul Brunet, Simon Docherty, Tobias Kapp ́e, Jurriaan Rot, Jana Wagemaker, and Fabio Zanasi.

DyNetKAT: An Algebra of Dynamic Networks

“…This motivates our next design constraint, namely, to build upon NetKAT in a hierarchical manner and without redefining its semantics. This constraint should not be taken lightly as the challenges in the recent concurrent extensions of NetKAT demonstrated [11,18,21]. We will elaborate on this point, in the presentation of our syntax and semantics.…”

“…A number of concurrent extensions of NetKAT have been introduced to date [11,18,21]. These extensions followed different design decisions than the present paper and a comparison of their approaches with ours is provided in Section 2; however, the most important difference lies in the fact that inspired by earlier abstractions in this domain [17], we were committed to create different layers for data-plane flows and dynamic updates such that every data-plane packet observes a single set of flow tables through its flight through the network.…”

DyNetKAT: An Algebra of Dynamic Networks

“…This motivated our next design constraint, namely, to build upon NetKAT in a hierarchical manner and without redefining its semantics. This constraint should not be taken lightly as the challenges in the recent concurrent extensions of NetKAT demonstrated [22,27,13]. We will elaborate on this point, in the presentation of our syntax and semantics.…”

“…A number of concurrent extensions of NetKAT have been introduced to date [22,27,13]. These extensions followed different design decisions than the present paper and a comparison of their approaches with ours is provided in Section 2; however, the most important difference lies in the fact that inspired by earlier abstractions in this domain [21], we were committed to create different layers for data-plane flows and dynamic updates such that every data-plane packet observes a single set of flow tables through its flight through the network.…”