Abstract
Complexc oncurrent behaviours that cannot be handled by causal partial orders are frequently modelled by a relational structures (X,<,衇), where X is a set (of event occurrences), < is causality and 衇 is weak causality relation ([5][9][7][13] and others). It was shown in [7] that the complex case require the pair of relations <> and 衇, where <> is commutativity, however no axioms for the pair <>, 衇 were given. We present such axioms under the assumption that observations of concurrent behaviours are modelled by stratified partial orders (step-sequences).
Partially supported by NSERC of Canada Grant and CITO of Ontario Grant.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
U. Abraham, S. Ben-David, M. Magodor, On global-time and inter-process communication, in Semantics for Concurrency, Workshops in Computing, Springer 1990, 311–323.
P. Baldan, N. Busi, A. Corradini, M. Pinna, Functorial Concurrent Semantics for Petri Nets with Read and Inhibitor Arcs, Lecture Notes in Computer Science 1877, Springer 2000, 115–127.
E. Best, F. de Boer, C. Palamedissi, Partial Order and SOS Semantics for Linear Constraint Programs, Lecture Notes in Computer Science 1282, Springer 1997, 256–273.
P. C. Fishburn, Intransitive indifference with unequal indifference intervals, J. Math. Psych. 7 (1970) 144–149.
H. Gaifman, V. Pratt, Partial order models of concurrency and the computation of functions, Proc. of LICS’87, 72–85.
R. Janicki and M. Koutny, Invariants and Paradigms of Concurrency Theory. Proc. of PARLE’91, Lecture Notes in Computer Science 506(1991), 59–74.
R. Janicki and M. Koutny, Structure of Concurrency, Theoretical Computer Science 112 (1993), 5–52.
R. Janicki and M. Koutny, Semantics of Inhibitor Nets, Information and Computation, 123, 1(1995), 1–16.
R. Janicki and M. Koutny, Fundamentals of modelling concurrency using discrete relational structures, Acta Informatica, 34, 367–388, 1997.
R. Janicki and M. Koutny, On Causality Semantics of Nets with Priorities, Fundamenta Informaticae 38(1999), 222–255.
J. Kleijn, M. Koutny, Process Semantics of P/T-Nets with Inhibitor Arcs, Lecture Notes in Computer Science 1825, Springer 2000, 261–281.
H. Klaudel, F. Pommereau, A Class of Composable and Preemptible High-Level Petri Nets with an Application to a Multi-Tasking System, Fundamenta Informaticae, to appear.
L. Lamport, The mutual exclusion problem: Part I— a theory of interprocess communication; Part II— statements and solutions, Joural of ACM 33,2 (1986) 313–326.
L. Lamport, What It Means for a Concurrent Programm to Satisfy a Specification: Why No One Has Specified Priority, Proc. 12th ACM Symp. on Programming Languages, 1985, 78–83.
M. Pietkiewicz-Koutny, The Synthesis Problem for Elementary Net Systems, Fundamenta Informaticae 40,2,3 (1999) 310–327.
E. Szpilrajn, Sur l’extension de l’ordre partial, Fundamenta Mathematicae 16(1930), 386–389.
W. Vogler, Timed Testing of Concurrent Systems, Information and Computation 121(1995), 149–171.
W. Vogler, Partial Order Semantics and Inhibitor Arcs, Lecture Notes in Computer Science 1295, Springer 1997, 508–517.
R. Wollowski, J. Beister, Precise Petri Net Modelling of Critical Races in Asynchronous Arbiters and Synchronizers, Proc. 1 st Workshop on Hardware Design and Petri Nets, Lisbon 1998, 46–65.
R. Wollowski, J. Beister, Comprehensive Causal Specification of Asynchronous Controller and Arbiter Behaviour, in A. Yakovlev, L. Gomes, L. Lavagno (eds.) Hardware Design and Petri Nets, Kluwer 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Guo, G., Janicki, R. (2002). Modelling Concurrent Behaviours by Commutativity and Weak Causality Relations* . In: Kirchner, H., Ringeissen, C. (eds) Algebraic Methodology and Software Technology. AMAST 2002. Lecture Notes in Computer Science, vol 2422. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45719-4_13
Download citation
DOI: https://doi.org/10.1007/3-540-45719-4_13
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44144-1
Online ISBN: 978-3-540-45719-0
eBook Packages: Springer Book Archive