Pomsets with Boxes: Protection, Separation, and Locality in Concurrent Kleene Algebra
FSCD
in Paris,
July 2020
Concurrent Kleene Algebra is an elegant tool for equational reasoning about concurrent programs. An important feature of concurrent programs that is missing from CKA is the ability to restrict legal interleavings. To remedy this we extend the standard model of CKA, namely pomsets, with a new feature, called boxes, which can specify that part of the system is protect from outside interference. We study the algebraic properties of this new model. Another drawback of CKA is that the language used for expressing properties of programs is the same as that which is used to express programs themselves. This is often too restrictive for practical purposes. We provide a logic, `pomset logic', that is an assertion language for specifying such properties, and which is interpreted on pomsets with boxes. We develop the basic metatheory for the relationship between pomset logic and CKA, including frame rules to support local reasoning, and illustrate this relationship with simple examples.
Related talks  
Avancées récentes sur les algèbres de Kleene concurrentes
séminaire du LACL
in Créteil,
December 2021
(in French)
.

More  
Recent developments in concurrent Kleene algebra
JetBrains Research
in St Petersburg (remote talk),
October 2021
.

More  
Avancées récentes sur les algèbres de Kleene concurrentes
Séminaire MAREL
in Montpellier,
April 2021
.

More  
Avancées récentes sur les algèbres de Kleene concurrentes
Séminaire ACADIE
in Toulouse,
April 2021
.

More  
Observations and locality in distributed processes
IRIS scientific meeting
in London,
March 2021
.

More  
Avancées récentes sur les algèbres de Kleene concurrentes
séminaire LIRICA
in Marseille,
January 2021
(in French)
.

More  
Avancées récentes sur les algèbres de Kleene concurrentes
Séminaire LOVE
in Paris,
January 2021
.

More  
Recent developments in concurrent Kleene algebra
IRIS scientific meeting
in London,
December 2020
.

More  
Recent developments in concurrent Kleene algebra
Séminaire PPS
in Paris,
June 2020
.

More  
Pomsets with boxes: towards Atomic CKA
Highlights
in Warsaw,
September 2019
.

More  
Pomset languages and concurrent Kleene algebra
Theory seminar  QMU
in London,
February 2018
.

More  
Pomset languages and concurrent Kleene algebras
Séminaire automates
in Paris,
November 2017
.

More  
On Decidability of Concurrent Kleene Algebra
CONCUR
in Berlin,
September 2017
.

More  
Related papers  
Equivalence checking for weak biKleene algebra
(in LMCS 2021)
with Tobias Kappé, Alexandra Silva, Bas Luttik and Fabio Zanasi. 
More  
Partially Observable Concurrent Kleene Algebra
(in CONCUR 2020)
with Jana Wagemaker, Simon Docherty, Jurriaan Rot, Tobias Kappé and Alexandra Silva. 
More  
Concurrent Kleene Algebra with Observations: From Hypotheses to Completeness
(in FoSSaCS 2020)
with Tobias Kappé, Alexandra Silva, Fabio Zanasi and Jana Wagemaker. 
More  
Pomsets with Boxes: Protection, Separation, and Locality in Concurrent Kleene Algebra
(in FSCD 2020)
with David Pym. 
More  
On SeriesParallel Pomset Languages: Rationality, ContextFreeness and Automata
(in JLAMP 2019)
with Tobias Kappé, Alexandra Silva, Bas Luttik and Fabio Zanasi. 
More  
Kleene Algebra with Observations
(in CONCUR 2019)
with Tobias Kappé, Alexandra Silva, Fabio Zanasi, Jurriaan Rot and Jana Wagemaker. 
More  
Concurrent Kleene Algebra: Free Model and Completeness
(in ESOP 2018)
with Tobias Kappé, Alexandra Silva and Fabio Zanasi. 
More  
Brzozowski Goes Concurrent  A Kleene Theorem for Pomset Languages
(in CONCUR 2017)
with Tobias Kappé, Alexandra Silva, Bas Luttik and Fabio Zanasi. 
More  
On Decidability of Concurrent Kleene Algebra
(in CONCUR 2017)
with Damien Pous and Georg Struth. 
More 