Verigraph: A System for Specification and Analysis of Graph Grammars

On the Essence of Parallel Independence for the Double-Pushout and Sesqui-Pushout Approaches

“…Here and in the next section we compare the performance of the three conditions based on their implementation in the Verigraph system and on their use, in various scenarios, for some concrete grammars defined in categories of typed graphs. Verigraph [9] is implemented in Haskell, exploiting its abstraction mechanisms to promote separation between abstract and concrete code. This allows the algorithms for checking parallel independence to be implemented at an abstract level (based on arrows and composition) as an almost direct translation of categorical diagrams and definitions.…”

“…The e cient verification of parallel independence is important for the analysis of graph transformation systems. It is needed for example in Critical Pair Analysis, a static analysis technique originally introduced in term rewriting systems [15] and, starting with [20], widely used also in graph transformation and supported by some tools [22,9]. It relies on the generation of all possible critical pairs, i.e.…”

“…In the second part of the paper we report on some experimental evaluations of the complexity of verifying parallel independence according with the three conditions. They have been implemented in Verigraph, a framework for the specification and verification of graph transformation systems written in Haskell, under development at the Universidade Federal do Rio Grande do Sul [9]. Since the current version of Verigraph does not support Sesqui-Pushout transformation, only left-linear rules are considered in the evaluation.…”

Parallel Independence in Attributed Graph Rewriting

“…When two transformations are involved, with rules r 1 and r 2 , this takes the form of the diamond property and is known as the Local Church-Rosser Problem [7]; it consists in finding a condition (called parallel independence) on direct transformations H 1 − → H. It is obvious that non overlapping redexes always entail parallel independence, the difficulty of the problem is that the reverse does not hold and that, depending on the rules, some amount of overlap may be allowed. The notion of parallel independence is also instrumental in defining Critical Pairs (as pairs of transformations that are not parallel independent) that are central in proving confluence of sets of production rules [14,8].…”