On First-Order Fragments for Mazurkiewicz Traces

Mazurkiewicz traces form a model for concurrency. Temporal logic st-order logic are important tools in order to deal with the abstract behavior of such systems. Since typical properties can be described by rather simple logical formulas one is interested in logical fragments. One focus of this paper is unary temporal logic and first-order logic in two variables. Over words, this corresponds to the variety of finite monoids called DA. However, over Mazurkiewicz traces it is crucial whether traces are given as dependence graphs or as partial orders (over words these notions coincide). The main technical contribution is a generalization of important characterizations of DA from words to dependence graphs, whereas the use of partial orders leads to strictly larger classes. As a consequence we can decide whether a first-order formula over dependence graphs is equivalent to a first-order formula in two variables. The corresponding result for partial orders is not known. This difference...

• Type: Journal
• Year: 2007
• Where: FUIN
• Authors: Volker Diekert, Martin Horsch, Manfred Kufleitner
• Keywords: Dependence Graphs, FUIN 2007, Logic, Partial Orders