TY  - JOUR
A1  - Möller, Bernhard
A1  - Hoare, Tony
A1  - Müller, Martin E.
A1  - Struth, Georg
T1  - A discrete geometric model of concurrent program execution
T2  - Lecture Notes in Computer Science
N2  - A trace of the execution of a concurrent object-oriented program can be displayed in two-dimensions as a diagram of a non-metric finite geometry. The actions of a programs are represented by points, its objects and threads by vertical lines, its transactions by horizontal lines, its communications and resource sharing by sloping arrows, and its partial traces by rectangular figures. We prove informally that the geometry satisfies the laws of Concurrent Kleene Algebra (CKA); these describe and justify the interleaved implementation of multithreaded programs on computer systems with a lesser number of concurrent processors. More familiar forms of semantics (e.g., verification-oriented and operational) can be derived from CKA. Programs are represented as sets of all their possible traces of execution, and non-determinism is introduced as union of these sets. The geometry is extended to multiple levels of abstraction and granularity; a method call at a higher level can be modelled by a specification of the method body, which is implemented at a lower level. The final section describes how the axioms and definitions of the geometry have been encoded in the interactive proof tool Isabelle, and reports on progress towards automatic checking of the proofs in the paper.
Y1  - 2017
UR  - https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/58731
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-587318
SN  - 9783319522272
SN  - 9783319522289
SN  - 0302-9743
SN  - 1611-3349
VL  - 10134
SP  - 1
EP  - 25
PB  - Springer International
CY  - Cham
ER  -