Affiliations: [a] Department of Computing and Software, McMaster University, Hamilton, ON, L8S 4K1, Canada | [b] LIACS, Leiden University, P.O.Box 9512, NL-2300 RA Leiden, The Netherlands | [c] School of Computing Science, Newcastle University, Newcastle upon Tyne, NE1 7RU, U.K. | [d] Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toruń, Chopina 12/18, Poland. [email protected]
Note: [*] Address for correspondence: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toruń, Chopina 12/18, Poland.
Abstract: Non-interleaving semantics of concurrent systems is often expressed using posets, where causally related events are ordered and concurrent events are unordered. Each causal poset describes a unique concurrent history, i.e., a set of executions, expressed as sequences or step sequences, that are consistent with it. Moreover, a poset captures all precedence-based invariant relationships between the events in the executions belonging to its concurrent history. However, concurrent histories in general may be too intricate to be described solely in terms of causal posets. In this paper, we introduce and investigate generalised mutex order structures which can capture the invariant causal relationships in any concurrent history consisting of step sequence executions. Each such structure comprises two relations, viz. interleaving/mutex and weak causality. As our main result we prove that each generalised mutex order structure is the intersection of the step sequence executions which are consistent with it.
