TY  - JOUR
A1  - Hoare, Tony
A1  - van Staden, Stephan
A1  - Möller, Bernhard
A1  - Struth, Georg
A1  - Zhu, Huibiao
T1  - Developments in concurrent Kleene algebra
T2  - Journal of Logical and Algebraic Methods in Programming
N2  - This report summarises the background and recent
progress in the research of its co-authors. It is aimed at the
construction of links between algebraic presentations of the
principles of programming and the exploitation of concurrency in
modern programming practice. The signature and laws of a Concurrent Kleene Algebra (CKA) largely overlap with those of a Regular Algebra, with the addition of concurrent composition and a few simple laws for it. They are re-interpreted here in application to computer programs.   The inclusion relation for regular expressions is re-interpreted as a refinement ordering, which supports a stepwise contractual approach to software system design and to program debugging.

The laws are supported by a hierarchy of models, applicable and
adaptable to a range of different purposes and to a range of different
programming languages.  The algebra is presented in three tiers. The
bottom tier defines traces of program execution, represented as sets
of events that have occurred in a particular run of a program; the
middle tier defines a program as the set of traces of all its possible
behaviours. The top tier introduces additional incomputable
operators, which are useful for describing the desired or undesired
properties of computer program behaviour. The final sections outline
directions in which further research is needed.
Y1  - 2016
UR  - https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/68900
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-689008
SN  - 2352-2208
VL  - 85
IS  - 4
SP  - 617
EP  - 636
PB  - Elsevier BV
ER  -