Modelling concurrency with comtraces and generalized comtraces

Abstract

Comtraces (combined traces) are extensions of Mazurkiewicz traces that can model the "not later than" relationship. In this paper, we first introduce the novel notion of generalized comtraces, extensions of comtraces that can additionally model the "non-simultaneously" relationship. Then we study some basic algebraic properties and canonical reprentations of comtraces and generalized comtraces. Finally we analyze the relationship between generalized comtraces and generalized stratified order structures. The major technical contribution of this paper is a proof showing that generalized comtraces can be represented by generalized stratified order structures.

Modeling concurrency with interval traces

“…As a consequence, stratified orders and step sequences can uniquely represent each other (cf. [Janicki and Koutny [1995]; Janicki and Lê [2011]; Lê [2011]…”

“…More details can be found in for example in [Janicki and Koutny [1995]; Janicki et al [2010]; Janicki and Lê [2011]]. …”

“…P Stratified order structures were independently introduced in [Gaifman and Pratt [1987]] and [Janicki and Koutny [1991]]. Their comprehensive theory has been presented in [Janicki [2008]; Janicki and Koutny [1997]; Janicki and Lê [2011]; Kleijn and Koutny [2008]]. …”

“…It is interpreted as the proof of the claim that stratified order structures uniquely represent sets of equivalent system runs, provided that the system's operational semantics can be fully described in terms of stratified orders (see [Janicki [2008]; Janicki and Koutny [1997]; Janicki et al [2010]; Janicki and Lê [2011]; Kleijn and Koutny [2008]] for details).…”

“…, is called an equational monoid (see [Janicki and Lê [2011]; Lê [2011]; Ochmański [1995]] for more details).…”