Abstract
Interval-order partially ordered multisets with interfaces (ipomsets) have shown to be a versatile model for executions of concur- rent systems in which both precedence and concurrency need to be taken into account. In this paper, we develop a presentation of ipomsets as generated by a graph of certain discrete ipomsets (starters and terminators) under the relation which composes subsequent starters and subsequent ter- minators. Using this presentation, we show that also subsumptions are generated by elementary relations. We develop a similar correspondence on the automata side, relating higher-dimensional automata, which gen- erate ipomsets, and ST-automata, which generate step sequences, and their respective languages.