Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-18T12:20:05.126Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis of permutation equivalence in $\mathcal{M}$-adhesive transformation systems with negative application conditions

Published online by Cambridge University Press:  26 June 2014

FRANK HERMANN ,
ANDREA CORRADINI  and
HARTMUT EHRIG
FRANK HERMANN
Affiliation:
Institut für Softwaretechnik und Theoretische Informatik, Technische Universität Berlin, Berlin, Germany and Interdisciplinary Centre for Security, Reliability and Trust, University of Luxembourg, Luxembourg Email: frank@cs.tu-berlin.de
ANDREA CORRADINI
Affiliation:
Dipartimento di Informatica, Università di Pisa, Pisa, Italy Email: andrea@di.unipi.it
HARTMUT EHRIG
Affiliation:
Institut für Softwaretechnik und Theoretische Informatik, Technische Universität Berlin, Berlin, Germany Email: ehrig@cs.tu-berlin.de
Get access Rights & Permissions [Opens in a new window]

Abstract

$\mathcal{M}$-adhesive categories provide an abstract framework for a large variety of specification frameworks for modelling distributed and concurrent systems. They extend the well-known frameworks of adhesive and weak adhesive HLR categories and integrate high-level constructs such as attribution as in the case of typed attributed graphs.

In the current paper, we investigate $\mathcal{M}$-adhesive transformation systems including negative application conditions (NACs) for transformation rules, which are often used in applications. For such systems, we propose an original equivalence on transformation sequences, called permutation equivalence, that is coarser than the classical switch equivalence. We also present a general construction of deterministic processes for $\mathcal{M}$-adhesive transformation systems based on subobject transformation systems. As a main result, we show that the process obtained from a transformation sequence identifies its equivalence class of permutation-equivalent transformation sequences. Moreover, we show how the analysis of this process can be reduced to the analysis of the reachability graph of a generated Place/Transition Petri net. This net encodes the dependencies between rule applications of the transformation sequence, including the inhibiting effects of the NACs.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 24 , Issue 4: Structure Transformation , August 2014 , 240409
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adámek, J., Herrlich, H and Strecker, G. (1990) Abstract and Concrete Categories, Wiley.Google Scholar
Baldan, P. (2000) Modelling Concurrent Computations: from Contextual Petri Nets to Graph Grammars, Ph.D. thesis, Computer Science Department, University of Pisa.Google Scholar
Baldan, P., Busi, N., Corradini, A and Pinna, G. M. (2004) Domain and event structure semantics for Petri nets with read and inhibitor arcs. Theoretical Computer Science 323 (1-3)129–189.CrossRefGoogle Scholar
Baldan, P., Corradini, A., Heindel, T., König, B and Sobociński, P. (2006) Processes for Adhesive Rewriting Systems. In: Aceto, L. and Ingólfsdóttir, A. (eds.) Proceedings FoSSaCS'06. Springer-Verlag Lecture Notes in Computer Science 3921 202–216.Google Scholar
Braatz, B., Ehrig, H., Gabriel, K and Golas, U. (2010) Finitary $\mathcal{M}$-Adhesive Categories. In: Ehrig, H., Rensink, A., Rozenberg, G and Schürr, A. (eds.) Proceedings ICGT'10. Springer-Verlag Lecture Notes in Computer Science 6372 234–249.Google Scholar
Brandt, C., Hermann, F and Engel, T. (2009) Modeling and Reconfiguration of critical Business Processes for the purpose of a Business Continuity Management respecting Security, Risk and Compliance requirements at Credit Suisse using Algebraic Graph Transformation. In: Proceedings Dynamic and Declarative Business Processes (DDBP 2009), IEEE Xplore Digital Library 64–71.Google Scholar
Busi, N. and Pinna, G. M. (1999) Process semantics for Place/Transition nets with inhibitor and read arcs. Fundamenta Informaticae 40 (2-3)165–197.Google Scholar
Corradini, A., Hermann, F and Sobociński, P. (2008) Subobject Transformation Systems. Applied Categorical Structures 16 (3)389–419.CrossRefGoogle Scholar
Corradini, A., Montanari, U and Rossi, F. (1996) Graph processes. Fundamenta Informaticae 26 (3/4)241–265.Google Scholar
Ehrig, H., Ehrig, K., Prange, U and Taentzer, G. (2006) Fundamentals of Algebraic Graph Transformation, EATCS Monographs in Theoretical Computer Science, Springer-Verlag.Google Scholar
Ehrig, H., Golas, U and Hermann, F. (2010) Categorical Frameworks for Graph Transformation and HLR Systems based on the DPO Approach. Bulletin of the EATCS 102 111–121.Google Scholar
Ehrig, H., Pfender, M and Schneider, H. (1973) Graph-grammars: an algebraic approach. In: Book, R. (ed.) Switching and Automata Theory, IEEE Computer Society Press 167–180.Google Scholar
Freyd, P. and Scedrov, A. (1990) Categories, Allegories, North-Holland.Google Scholar
Habel, A., Heckel, R and Taentzer, G. (1996) Graph Grammars with Negative Application Conditions. Fundamenta Informaticae 26 (3/4)287–313.Google Scholar
Habel, A. and Pennemann, K.-H. (2009) Correctness of high-level transformation systems relative to nested conditions. Mathematical Structures in Computer Science 19 (2)245–296.CrossRefGoogle Scholar
Heindel, T. (2010) Hereditary Pushouts Reconsidered. In: Ehrig, H., Rensink, A., Rozenberg, G and Schürr, A. (eds.) Proceedings ICGT'10. Springer-Verlag Lecture Notes in Computer Science 6372 250–265.CrossRefGoogle Scholar
Hermann, F. (2009) Permutation Equivalence of DPO Derivations with Negative Application Conditions based on Subobject Transformation Systems. Electronic Communications of the EASST 16.Google Scholar
Hermann, F., Corradini, A., Ehrig, H and König, B. (2010) Efficient Analysis of Permutation Equivalence of Graph Derivations Based on Petri Nets. Electronic Communications of the EASST 29.Google Scholar
ISO/IEC (2004) ISO/IEC 15909-1:2004, Software and system engineering – High-level Petri nets – Part 1: Concepts, definitions and graphical notation, ISO/IEC.Google Scholar
Janicki, R. and Koutny, M. (1995) Semantics of inhibitor nets. Information and Computation 123 (1)1–16.CrossRefGoogle Scholar
Kastenberg, H., Hermann, F and Modica, T. (2006) Towards Translating Graph Transformation Systems by Model Transformation. Electronic Communications of the EASST 4.Google Scholar
Kleijn, H. C. M. and Koutny, M. (2004) Process semantics of general inhibitor nets. Information and Computation 190 (1)18–69.Google Scholar
Lack, S. and Sobociński, P. (2004) Adhesive Categories. In: Proceedings FOSSACS'04. Springer-Verlag Lecture Notes in Computer Science 2987 273–288.Google Scholar
Lack, S. and Sobociński, P. (2005) Adhesive and quasiadhesive categories. Theoretical Informatics and Applications 39 (3)511–545.CrossRefGoogle Scholar
Lambers, L. (2009) Certifying Rule-Based Models using Graph Transformation, Ph.D. thesis, Technische Universität Berlin.Google Scholar
Lambers, L., Ehrig, H., Orejas, F and Prange, U. (2008) Parallelism and Concurrency in Adhesive High-Level Replacement Systems with Negative Application Conditions. In: Proceedings of the ACCAT workshop at ETAPS 2007. Electronic Notes in Theoretical Computer Science 203 (6)43–66.Google Scholar
Meseguer, J. and Montanari, U. (1990) Petri Nets are Monoids. Information and Computation 88 (2)105–155.Google Scholar
Reisig, W. (1985) Petri Nets: An Introduction, EATCS Monographs on Theoretical Computer Science 4, Springer-Verlag.Google Scholar
Rozenberg, G. and Engelfriet, J. (1996) Elementary Net Systems. In: Reisig, W. and Rozenberg, G. (eds.) Lectures on Petri Nets I: Basic Models. Springer-Verlag Lecture Notes in Computer Science 1491 12–121.Google Scholar