Graph Transactions as Processes

Abstract

Abstract. Transactional graph transformation systems (t-gtss) have been recently proposed as a mild extension of the standard dpo approach to graph transformation, equipping it with a suitable notion of atomic execution for computations. A typing mechanism induces a distinction between stable and unstable items, and a transaction is defined as a shift-equivalence class of computations such that the starting and ending states are stable and all the intermediate states are unstable.The paper introduces an equivalent, yet more manageable definition of transaction based on graph processes. This presentation is used to provide a universal characterisation for the class of transactions of a given t-gts. More specifically, we show that the functor mapping a t-gts to a graph transformation system having as productions exactly the transactions of the original t-gts is the right adjoint to an inclusion functor.

Graph-based software specification and verification

“…In flat graph production systems, the order in which rules must be applicable is often directed by temporary graph elements that are then processed (e.g., propagated or deleted) by successive rule applications. Baldan et al [6,7] have introduced the notion of graph transactions in which they distinguish between stable and unstable graphs; the latter being graphs containing such temporary graph elements. A sequence of rule applications transforming one stable graph into another stable graph via unstable graphs only, is then considered a graph transaction.…”

“…A sequence of rule applications transforming one stable graph into another stable graph via unstable graphs only, is then considered a graph transaction. In fact, a graph transaction (in [7] called an abstract transaction) represents all possible orderings of the individual transformation steps of such a sequence that all result in the same (or isomorphic) graph. In many cases we are only interested in whether all reachable stable graphs satisfy specific properties.…”