WSEAS TRANSACTIONS on INFORMATION SCIENCE and APPLICATIONS DOI: 10.37394/23209.2020.17.13 Anthony Spiteri Staines Graph Drawing Approaches for Petri Net Models ANTHONY SPITERI STAINES Department of Computer Information Systems University of Malta MSIDA 2080 MALTA Abstract: - This work presents a theoretical perspective how to apply graph drawing approaches to Petri Net models. Section 1 is the introduction to the problem. Section 2 is the background and the motivation. This part explains why graph drawing approaches are useful for Petri net modelling. Section 3 is the problem definition. This part explains the main problem. Section 4 defines the proposed solutions and examples are given. Section 5 discusses results, findings and assumptions. Section 6 gives some conclusions. Key-Words: - Representation, Matrices, Ordinary Petri nets, System Modelling Received: February 27, 2020. Revised: July 3, 2020. Accepted: July 13, 2020. Published: July 16, 2020 1 Introduction Similar approaches could be used for nodes. Graph Graphs are useful tools for visualization. Their drawings can be heavily connected. intended use in the field of computing and There is the possibility for having cycles or a mathematics is vast. They can be used for formal cycle free drawing. The planarity or the representation. Graphs can be a fundamental orthogonality of the graph affects the shape and component of computer modelling such as the characteristics of the drawing [1]-[9]. The diagrammatic notations found in software modelling connectedness of the graphs determine how the and design [1]-[9]. They are useful to transform representation is and impacts the structure of the observations or mind concepts into actual graph. Sources and sinks in the graph determine the representation models that can be communicated to graph type. Polyline drawing approaches are useful different stakeholders. Graph research is not just for visibility representation. Rooted trees are special aimed at acquiring skills to solve known problems cases of graph drawings. Different algorithms like but also at dealing with different situations where divide and conquer, radial drawing, etc. can be used there is no proper expertise. Graphs can be used to for drawing rooted trees. The concepts of create cognitive maps. miniminality and maximalty, imply that when Graph drawing is a discovery process. It can be drawing a system different configurations exist [1]- used to discover the existence of different models [6]. It is possible to show the minimal form of the and patterns [1]. drawing or else the maximal form. In the minimal This work deals with the use of different forms form there is reduced detail however the notation is of graph modelling and drawing techniques. easier to understand, visualise and remember. It can Different techniques range from planar orientations, be aesthetically more pleasant and tidier. On the polyline drawings, acyclical representation, and other hand the maximal principle implies that as others to tree like structures that can be reduced, much detail as possible is captured in the notation. redrawn or re-improved. Different techniques and This work is limited to Petri net graph drawings algorithms are usable for compaction [6]-[10]. [12]-[16]. Petri nets are conventionally bipartite There are several ways for representing or digraphs that fall within the representation of drawing a graph. This sounds simple but many digraphs. They can be conventionally represented intricate complexities are involved in doing so. Even using many of the graph drawing mainstream the ‘simple’ task of inserting a node or an edge in a approaches. Which type of approach is best suited to model is actually not a simple task at all. Several drawing Petri net models? This is a difficult algorithms ranging from simple to complex ones are question to answer for the simple reason that every involved in this job. Several insertion rules or model is different. Simple Petri net drawings can strategies are available [1]. The insertion techniques take a variety of different shapes and forms. can use dummy, literal, clause, etc. type of edges. Structural representation is an important topic in computing. Structural complexity deals with formal E-ISSN: 2224-3402 110 Volume 17, 2020 WSEAS TRANSACTIONS on INFORMATION SCIENCE and APPLICATIONS DOI: 10.37394/23209.2020.17.13 Anthony Spiteri Staines methods but it is not necessarily limited just to networking, electrical engineering and even biology formal languages. Complexity can be evidenced in and chemistry (e.g. to show properties and reactions architectures, patterns, computer related structures of equations). and why not graphs? This is because graph models In literature, normally no particular style is represent system structures. Complexity is related to considered when the Petri nets are drawn. So they abstraction and representation too. The proper are drawn using an ad-hoc approach which is drawing of models is a reflection of the normally acceptable for the work being presented. understanding of complexity. Some problems might This work tries to give ideas on how Petri nets be unsolvable, however they can still be represented that are drawn can be aesthetically improved using graphically. Different models of computation are different drawing styles or approaches. The user is possible, graphical abstractions retain a universal given leeway for experimentation when drawing the characteristic and the models can withstand the test Petri net. By no means is the user restricted to using of time. the ideas given in this work. This work should serve Abstraction is the tool used to deal with as a source of inspiration and ideas that would allow complexity. Abstraction involves paradoxically the user to come up with a better forms and ideas for sacrificing many of the complex details and going presenting the models purely from the drawing point for a more limited one. Complex models that reflect of view. From the mathematical point of view the many details provide the suitable scenario for Petri net that is drawn would remain unmodified. abstraction. I.e. this work focuses on the visual style of the Petri Ideally the OCCAM razor principle of simplicity net. can be applied in this work. Simplification is not a As already stated it is impossible to cover all the simple task and requires considerable amount of material and ideas related to graph drawing in a book let alone a simple paper. Graph drawings are knowledge. This is evidenced by the vast amount of suitable for improving visualisation as t here are literature in the topic and the multitude of several different styles that can be used to represent algorithms that can be used for drawing and re- graphs. Petri net drawings in some instances are drawing these structures. Abstraction deals with very close to circuit schematic layouts. However the decomposing the problem into smaller counterparts end result and approval of the drawing lies in the that can be solved individually. user perception. User perception cannot be It is impossible to cover all the styles and measured or validated easily. E.g. why is a certain possibilities that exist in just one paper. Possibly not structure more attractive than another even if both even several books would do justice to the problem. are representative of the same thing? Having a good So this work is a small attempt that tries to strike a layout will enhance the readability of the structure. balance between drawing Petri nets and their There is the concept of added value when drawing a possible graph representations. graph. A graph that is perfectly drawn adds value to the work it is presented in. Users need to keep these 2 Background and Motivation principles in mind when using Petri net drawings. Petri nets are useful formalisms that share a dual A balanced approach needs to be found between identity having both a mathematical and graphical the aesthetical drawing of Petri nets and the representation. Petri nets [14]-[15] share several overdrawing or over engineering of these models. common features with digraphs [1],[2]. They are useful for representing static and dynamic 3 Problem Definition structures. They have found extensive use in As structures for visualisation and modelling, graph literature and in various fields. Graph drawings are representations and structures are useful tools for like syntactic glue that hold the system properties visualisation and modelling. Graphs have been together [1]-[11]. widely used in the field of requirements engineering There are several classes of Petri nets that follow and software engineering [1],[2]. different definitions and conventions. These classes The drawing and representation of Petri nets as range from elementary or simple classes to more graphs is not simple. The attractiveness of the structured and complex ones like coloured Petri nets drawing can be based on principles of layout, and higher order abstractions of Petri nets. Drawing simplification, abstraction and aesthetics. This will Petri nets is an easy task if the Petri net is limited in have a g reat impact on the usability. Most users size and scope. Petri nets are widely used in prefer to use a model that looks nice. Edges and literature and have found their place in different nodes that are properly represented add value to the fields of science ranging from computing, E-ISSN: 2224-3402 111 Volume 17, 2020 WSEAS TRANSACTIONS on INFORMATION SCIENCE and APPLICATIONS DOI: 10.37394/23209.2020.17.13 Anthony Spiteri Staines model. There are no standard established procedures 4 Proposed Solutions for Petri net drawing. A mixture of methods and As this work is an experiment several graph several styles can be used. From the graph drawing drawings will be classified and represented. The point of view, Petri net drawing is not ‘optimized’. proposed solutions have been derived from robust Sometimes the edges can be in part curves or approaches used in the field of graph drawing and straight lines, etc.