CKA : Concurrent Kleene Algebras
Concurrent Kleene algebra (CKA) is an algebraic framework to reason about concurrent programs. This project concerns itself with the study of this framework, and of its enhancements with extra features. The aim is to carry out sophisticated verification tasks using this language.
Test equations
How to use this :
Write an equation in the input field of the applet, and see its validity just to the right (a green tick meaning yes and a red cross meaning no).
Equations should be entered like this:
<expr1> <cmp> <expr2>
An expression can use strings as variables/letters, and the operations:
0
: the empty set1
: the empty process<expr1> + <expr2>
: the set union<expr1>  <expr2>
: the parallel product<expr1> . <expr2>
: the sequential product<expr1>*
: the unbounded sequential iteration<expr1>+
: the unbounded nonempty sequential iteration<expr1>{<int>}
: the fixed iteration. For instance,(a.b){3}
is a shorthand for(a.b).(a.b).(a.b)
You can also use brackets (...)
.
The valid comparaisons <cmp>
are:
<=
: loose inclusion>=
: converse of the loose inclusion<
: strict inclusion>
: converse of the strict inclusion=
: equality=/=
: negation of the equality<>
: means that the two expressions are incomparable, i.e. neither one of them is included in the other.
For instance, (ab)^+ . C + d < d + a.b.C + (da)
is an acceptable equation.
The tester
Net viewer
Detailled equation checking
≤ 
Net for the first expression:  Net for the second expression:  
Automaton of the accepting runs:  Product automaton:  
Related documents
Equation checker  
Sources  
Documentation  
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  
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  
Pomsets with Boxes: Protection, Separation, and Locality in Concurrent Kleene Algebra
FSCD
in Paris,
July 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 