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

Abstract

Parallel independence between transformation steps is a basic notion in the algebraic approaches to graph transformation, which is at the core of some static analysis techniques like Critical Pair Analysis. We propose a new categorical condition of parallel independence and show its equivalence with two other conditions proposed in the literature, for both left-linear and non-left-linear rules. Next we present some preliminary experimental results aimed at comparing the three conditions with respect to computational e ciency. To this aim, we implemented the three conditions, for left-linear rules only, in the Verigraph system, and used them to check parallel independence of pairs of overlapping redexes generated from some sample graph transformation systems over categories of typed graphs.

Sesqui-Pushout Rewriting: Concurrency, Associativity and Rule Algebra Framework

“…the cloning and fusing of vertices in graphs), this most general case is left for future work.SqPO Rewriting: Concurrency, Associativity and Rule Algebra Framework adhesive categories (see Assumption 1) in order to ensure certain technical properties necessary for our concurrency and associativity theorems to hold. To the best of our knowledge, apart from some partial results in the direction of developing a concurrency theorem for SqPO-type rewriting in [16,36,15], prior to this work neither of the aforementioned theorems had been available in the SqPO framework.Associativity of SqPO rewriting theories plays a pivotal role in our development of a novel form of concurrent semantics for these theories, the so-called SqPO-type rule algebras. Previous work on associative DPO-type rewriting theories [3, 5, 7] (see also [8]) has led to a category-theoretical understanding of associativity that may be suitably extended to the SqPO setting.…”

On the Essence and Initiality of Conflicts

“…In this paper, we contribute to this research thread by proposing a new characterization for the root causes of conflicts, called conflict essences, based on a recently proposed characterization of parallel independence [3]. In any adhesive category with strict initial object we show that having an empty conflict essence is equivalent to parallel independence, and that conflict essences are smaller than conflict reasons.…”

“…We start introducing parallel independence according to the so-called essential definition [3]. Definition 19 (Parallel Independence).…”

Equivalence and Independence in Controlled Graph-Rewriting Processes

“…Intuitively, two rule applications starting from the same graph are parallel independent if they can be sequentialized arbitrarily with isomorphic results. This property is captured categorically by the following definition [5].…”

“…As discussed in [5], this definition is equivalent to others proposed in literature, but does not need to compute the pushout complements to be checked.…”