The *GReTA* *–* **G***raph* *T***R***ansformation* **T***heory and* **A***pplications* virtual seminar series aims to serve as a platform for the international graph rewriting community, to promote recent developments and trends in the field, and to permit a regular networking and interaction between members of this community. Seminars are held twice a month in the form of Zoom sessions (some of which will be live-streamed to YouTube).

Several options are available to receive regular updates on the GReTA seminars:

- Subscribe to the GReTA YouTube channel.
- Subscribe to the GReTA Google Calendar (or alternatively import it in iCal format).
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We review the integration of (first-order) logic respectively nested conditions into graph transformation. Conditions can serve various purposes: they can constrain graph rewriting, symbolically specify sets of graphs, be used in query languages and in verification (for instance in Hoare logic and for behavioural equivalence checking). In the graph transformation community the formalism of nested graph conditions has emerged, that is, conditions which are equivalent to first-order logic, but directly integrate graphs and graph morphisms, in order to express constraints more succinctly. In this talk we also explain how the notion of nested conditions can be lifted from graph transformation systems to the setting of reactive systems as defined by Leifer and Milner. It turns out that some constructions for graph transformation systems (such as computing weakest preconditions and strongest postconditions and showing local confluence by means of critical pair analysis) can be done quite elegantly in the more general setting.

We present our on-going work on creating a practical modelling framework for chemistry based on Double Pushout graph transformation, and how it can be applied to analyse chemical systems. We will address important technical design decisions as well as the importance of methods inspired from Algorithm Engineering in order to reach the required efficiency of our implementation. We will present chemically relevant features that our framework provides (e.g. automatic atom tracing) as well as a set of chemical systems we investigated are currently investigating. If time allows we will discuss variations of graph transformation rule compositions and their chemical validity.

Graph rewriting systems are natural verification and validation tools: they provide visual, intuitive representations of complex systems while specifying the dynamic behaviour of the system in a formal way. In this talk we will describe the use of strategic port graph rewriting as a basis for the implementation of a visual modelling tool: PORGY. We will present attributed hierarchical port graphs (AHP) and a notion of strategic AHP-rewriting as a mechanism to model the behaviour of dynamic systems. The system modelled is represented by an initial graph and a collection of graph rewrite rules, together with a user-defined strategy to control the application of rules. The traditional operators found in strategy languages for term rewriting have been adapted to deal with the more general setting of graph rewriting, and some new constructs have been included in the strategy language to deal with graph traversal and management of rewriting positions in the graph. In the second part of the talk, we describe PORGY and give examples of application in the areas of biochemistry, social networks and finance.

We will review old and new results about confluence of GTS, without and with application conditions.

An overview presentation of the work we have been doing over the past years on MDEOptimiser, a tool that uses evolutionary search over EMF models to solve multi-objective optimisation problems. Graph transformations are used to encode mutation operators, opening interesting opportunities for automatically generating domain-specific mutation operators.

This will be an overview of our ongoing work on fast graph programs in the language GP 2. We will present programs which in some cases match the time complexity of graph algorithms in imperative languages. In other cases we need to assume that input graphs have a bounded degree, to reach the speed of conventional algorithms. This will be a one-hour joint talk with Graham Campbell (Newcastle University).A

Double Pushout (DPO) rewriting, the dominant model for graph rewriting, emerged in the early 70’s, strongly influenced at that time by graph grammars. Developed by Hartmut Ehrig and his many collaborators, graph rewriting was from the beginning based on category theory, with the major insight that the two basic rewriting constructions, namely matching and replacement, were intimately related to graph morphisms and their pushouts. A new model has emerged recently, so-called Composition based rewriting (Core), in which rewriting is based on a composition operator over directed rooted labelled graphs (drags), so that matching a drag G against a drag L amounts to compose L with some context drag C, and rewriting G with L -> R to compose R with C. We will describe Core for drags before to relate it precisely to DPO and extend it to adhesive categories of graphs and beyond. We will also show how to define composition abstractly in any category of graphs satisfying appropriate properties among which adhesivity (wrt monomorphisms). Major differences between DPO and Core will be discussed.

The *GReTA* seminars are hosted via Zoom. For security reasons, participation in a given seminar requires a **registration** (via the link provided in the announcement of the seminar). Upon completion of the registration form (asking for the name, affiliation and email address), a personalized Zoom meeting link will be sent. For convenience, sessions will be open *15 minutes prior* to the beginning of the seminar.

Please join the session with your camera and microphone enabled, noting that it will be the chairperson of the session who will then unmute your microphone for questions! If possible, please consider joining already during the 15 minutes prior to a given seminar, to ensure your Zoom setup is functioning properly.

Alternatively, if you prefer not to participate via Zoom, some seminars will be live-streamed to YouTube, where it will be possible to ask questions via the YouTube commenting functionality.

Each seminar will be hosted by a chairperson who will introduce the speaker, watch incoming questions and who will decide if and when to interrupt the speaker for questions, or which questions should be postponed to after the talk.

After each seminar, the main Zoom session will remain open for additional 30 minutes in order to allow for discussions and networking. Depending on the number of participants, it will be a possibility to gather into small breakout sessions as well.