The complexity of Petri net transformations

Bibliography: pages 124-127.This study investigates the complexity of various reduction and synthesis Petri net transformations. Transformations that preserve liveness and boundedness are considered. Liveness and boundedness are possibly the two most important properties in the analysis of Petri nets. Unfortunately, although decidable, determining such properties is intractable in the general Petri net. The thesis shows that the complexity of these properties imposes limitations on the power of any reduction transformations to solve the problems of liveness and boundedness. Reduction transformations and synthesis transformations from the literature are analysed from an algorithmic point of view and their complexity established. Many problems regarding the applicability of the transformations are shown to be intractable. For reduction transformations this confirms the limitations of such transformations on the general Petri net. The thesis suggests that synthesis transformations may enjoy better success than reduction transformations, and because of problems establishing suitable goals, synthesis transformations are best suited to interactive environments. The complexity of complete reducibility, by reduction transformation, of certain classes of Petri nets, as proposed in the literature, is also investigated in this thesis. It is concluded that these transformations are tractable and that reduction transformation theory can provide insight into the analysis of liveness and boundedness problems, particularly in subclasses of Petri nets

A categorical framework for concurrent, anticipatory systems

A categorical semantic domain is constructed for Petri nets which satisfies the diagonal compositionality requirement with respect to anticipations, i.e., Petri nets are equipped with a compositional anticipation mechanism (vertical compositionality) that distributes through net combinators (horizontal compositionality). The anticipation mechanism is based on graph transformations (single pushout approach). A finitely bicomplete category of partial Petri nets and partial morphisms is introduced. Classes of transformations stand for anticipations. The composition of anticipations (i.e., composition of pushouts) is defined, leading to a category of nets and anticipations which is also complete and cocomplete. Since the anticipation operation composes, the vertical compositionality requirement of Petri nets is achieved. Then, it is proven that the anticipation also satisfies the horizontal compositionality requirement. A specification grammar stands for a system specification and the corresponding induced subcategory of nets and anticipation's stands for ali possible dynamic anticipation's ofthe system (objects) and their relationship (morphims)

Automating the transformation-based analysis of visual languages

The final publication is available at Springer via http://dx.doi.org/10.1007/s00165-009-0114-yWe present a novel approach for the automatic generation of model-to-model transformations given a description of the operational semantics of the source language in the form of graph transformation rules. The approach is geared to the generation of transformations from Domain-Specific Visual Languages (DSVLs) into semantic domains with an explicit notion of transition, like for example Petri nets. The generated transformation is expressed in the form of operational triple graph grammar rules that transform the static information (initial model) and the dynamics (source rules and their execution control structure). We illustrate these techniques with a DSVL in the domain of production systems, for which we generate a transformation into Petri nets. We also tackle the description of timing aspects in graph transformation rules, and its analysis through their automatic translation into Time Petri netsWork sponsored by the Spanish Ministry of Science and Innovation, project METEORIC (TIN2008-02081/TIN) and by the Canadian Natural Sciences and Engineering Research Council (NSERC)

Transfer of Local Confluence and Termination between Petri Net and Graph Transformation Systems Based on M-Functors: Extended Version

Recently, a formal relationship between Petri net and graph transformation systems has been established using the new framework of M-functors F : (C1;M1) -> (C2;M2) between M-adhesive categories. This new approach allows to translate transformations in (C1;M1) into corresponding transformations in (C2;M2) and, vice versa, to create transformations in (C1;M1) from those in (C2;M2). This is helpful because our tool for reconfigurable Petri nets, the RON-tool, performs the analysis of Petri net transformations by analyzing corresponding graph transformations using the AGG-tool. Up to now, this correspondence has been implemented as a converter on an informal level. The formal correspondence results given by our framework make the RON-tool more reliable. In this paper we extend this framework to the transfer of local confluence, termination and functional behavior. In particular, we are able to create these properties for transformations in (C1;M1) from corresponding properties of transformations in (C2;M2), where (C1;M1) are Petri nets with individual tokens and (C2;M2) typed attributed graphs. This allows us to apply the wellknown critical pair analysis for typed attributed graph transformations supported by the AGG-tool in order to analyze these properties for Petri net transformations

Transfer of Local Confluence and Termination between Petri Net and Graph Transformation Systems Based on M-Functors

Recently, a formal relationship between Petri net and graph transformation systems has been established using the new framework of M-functors F : (C1;M1) -> (C2;M2) between M-adhesive categories. This new approach allows to translate transformations in (C1;M1) into corresponding transformations in (C2;M2) and, vice versa, to create transformations in (C1;M1) from those in (C2;M2). This is helpful because our tool for reconfigurable Petri nets, the RONtool, performs the analysis of Petri net transformations by analyzing corresponding graph transformations using the AGG-tool. Up to now, this  correspondence has been implemented as a converter on an informal level. The formal correspondence results given by our framework make the RON-tool more reliable.In this paper, we extend this framework to the transfer of local confluence, termination and functional behavior. In particular, we are able to create these properties for transformations in (C1;M1) from corresponding properties of transformations in (C2;M2), where (C1;M1) are Petri nets with individual tokens and (C2;M2) typed attributed graphs. This allows us to apply the well-known critical pair analysis for typed attributed graph transformations supported by the AGG-tool in order to analyze these properties for Petri net transformations

Formal Relationship between Petri Net and Graph Transformation Systems based on Functors between M-adhesive Categories

Various kinds of graph transformations and Petri net transformation systems are examples of M-adhesive transformation systems based on M-adhesive categories, generalizing weak adhesive HLR categories. For typed attributed graph transformation systems, the tool environment AGG allows the modeling, the simulation and the analysis of graph transformations. A corresponding tool for Petri net transformation systems, the RON-Environment, has recently been developed which implements and simulates Petri net transformations based on corresponding graph transformations using AGG. Up to now, the correspondence between Petri net and graph transformations is handled on an informal level. The purpose of this paper is to establish a formal relationship between the corresponding M-adhesive transformation systems, which allow the translation of Petri net transformations into graph transformations with equivalent behavior, and, vice versa, the creation of Petri net transformations from graph transformations. Since this is supposed to work for different kinds of Petri nets, we propose to define suitable functors, called M-functors, between different M-adhesive categories and to investigate properties allowing us the translation and creation of transformations of the corresponding M-adhesive transformation systems

Functors between M-adhesive Categories Applied to Petri Net and Graph Transformation Systems

Various kinds of graph transformations and Petri net transformation systems are examples of M-adhesive transformation systems based on M-adhesive categories, generalizing weak adhesive HLR categories. For typed attributed graph transformation systems, the tool environment AGG allows the modeling, the simulation and the analysis of graph transformations. A corresponding tool for Petri net transformation systems, the RON-Environment, has recently been developed which implements and simulates Petri net transformations based on corresponding graph transformations using AGG. Up to now, the correspondence between Petri net and graph transformations is handled on an informal level. The purpose of this paper is to establish a formal relationship between the corresponding M-adhesive transformation systems, which allow the translation of Petri net transformations into graph transformations with equivalent behavior, and, vice versa, the creation of Petri net transformations from graph transformations. Since this is supposed to work for different kinds of Petri nets, we propose to define suitable functors, called M-functors, between different M-adhesive categories and to investigate properties allowing us the translation and creation of transformations of the corresponding M-adhesive transformation systems

ReConNet: A Tool for Modeling and Simulating with Reconfigurable Place/Transition Nets

In this contribution we present a tool for modeling and simulation with reconfigurable Petri nets. Taking the idea of algebraic graph transformations to marked Petri nets we obtain Petri nets whose net structure can be changed dynamically. The rule-based change of the net structure enables the adequate modeling of complex, dynamic structures as for example of  the scenarios of the Living Place Hamburg. The tool \reconnet \ uses decorated  place/transition nets that are extended by various annotations. Especially, they  have transition labels that may change when the transition fires. The  transformation approach is based on the well-known algebraic transformation approach, but here we use a variant, namely the cospan approach, that inverts the relation between  left- and right-hand sides and interface in the  rules

Algebraic High-Level Nets and Processes Applied to Communication Platforms

Petri nets are well-known to model communication structures and algebraic specifications for modeling data types. Algebraic High-Level (AHL) nets are defined as integration of Petri nets with algebraic data types, which allows to model the communication structure and the data flow within one modelling framework. Transformations of AHL-nets – inspired by the theory of graph transformations – allow in addition to modify the communication structure. Moreover, highlevel processes of AHL-nets capture the concurrent semantics of AHL-nets in an adequate way. Altogether we obtain a powerful integrated formal specification technique to model and analyse all kinds of communication based systems. In this paper we give a comprehensive introduction of this framework. This includes main results concerning parallel independence of AHL-transformations and the transformation and amalgamation of AHL-occurrence nets and processes. Moreover, we show how this can be applied to model and analyse modern communication and collaboration platforms like Google Wave and Wikis. Especially we show how the Local Church-Rosser theorem for AHL-net tranformations can be applied to ensure the consistent integration of different platform evolutions. Moreover, the amalgamation theorem for AHL-processes shows under which conditions we can amalgamate waves of different Google Wave platforms in a compositional way

Algebraic High-Level Nets as Weak Adhesive HLR Categories

Adhesive high-level replacement (HLR) systems have been recently introduced as a new categorical framework for double pushout transformations. Algebraic high-level nets combine algebraic specifications with Petri nets to allow the modelling of data, data flow and data changes within the net. In this paper, we show that algebraic high-level schemas and nets fit well into the context of weak adhesive HLR categories. This allows us to apply the developed theory also to algebraic high-level net transformations