Hasse Diagrams of Combined Traces

One of the standard ways to represent concurrent behaviours is to use concepts originating from language theory, such as traces and comtraces. Traces can express notions such as concurrency and causality, whereas comtraces can also capture weak causality and simultaneity. This paper is concerned with the development of efficient data structures and algorithms for manipulating comtraces. We introduce Hasse diagrams for comtraces which are a generalisation of Hasse diagrams defined for partial orders and traces, and develop an efficient algorithm for deriving them from language theoretic representations of comtraces. We also explain how the new representation of comtraces can be used to implement efficiently some basic operations on comtraces.