Modeling Interval Order Structures with Partially Commutative Monoids

Interval order structures are useful tools to model abstract concurrent histories, i.e. sets of equivalent system runs, when system runs are modeled with interval orders. The paper shows how interval order structures can be modeled by partially commutative monoids, called interval traces.

[1]  A. Mazurkiewicz Concurrent Program Schemes and their Interpretations , 1977 .

[2]  E. Szpilrajn Sur l'extension de l'ordre partiel , 1930 .

[3]  Maciej Koutny,et al.  Structure of Concurrency , 1991, Theor. Comput. Sci..

[4]  Maciej Koutny,et al.  Fundamentals of modelling concurrency using discrete relational structures , 1997, Acta Informatica.

[5]  Wlodzimierz M. Zuberek,et al.  Timed Petri nets and preliminary performance evaluation , 1980, ISCA '80.

[6]  Grzegorz Rozenberg,et al.  Behavioural notions for elementary net systems , 1989, Distributed Computing.

[7]  Leslie Lamport,et al.  The mutual exclusion problem: part I—a theory of interprocess communication , 1986, JACM.

[8]  Dai Tri Man Le,et al.  On Three Alternative Characterizations of Combined Traces , 2010, Fundam. Informaticae.

[9]  Maciej Koutny,et al.  Quotient Monoids and Concurrent Behaviours , 2010, Scientific Applications of Language Methods.

[10]  Carlos Martín-Vide,et al.  Scientific Applications of Language Methods , 2010, Mathematics, Computing, Language, and Life: Frontiers in Mathematical Linguistics and Language Theory.

[11]  Dai Tri Man Le,et al.  Modelling concurrency with comtraces and generalized comtraces , 2009, Inf. Comput..

[12]  Maciej Koutny,et al.  Semantics of Inhibitor Nets , 1995, Inf. Comput..

[13]  Maciej Koutny,et al.  Formal Languages and Concurrent Behaviours , 2008, New Developments in Formal Languages and Applications.

[14]  P. Fishburn Intransitive indifference with unequal indifference intervals , 1970 .

[15]  Ryszard Janicki,et al.  Relational structures model of concurrency , 2008, Acta Informatica.

[16]  Wojciech Zielonka,et al.  The Book of Traces , 1995 .

[17]  Maciej Koutny,et al.  Process semantics of general inhibitor nets , 2004, Inf. Comput..

[18]  Antoni W. Mazurkiewicz,et al.  Introduction to Trace Theory , 1995, The Book of Traces.

[19]  Shai Ben-David,et al.  On Global-Time and Inter-process Communication , 1990 .

[20]  Maciej Koutny,et al.  Invariants and paradigms of concurrency theory , 1991, Future Gener. Comput. Syst..