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Pattern Matching and Membership for Hierarchical Message Sequence Charts

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Abstract

Several formalisms and tools for software development use hierarchy in system design, for instance statecharts and diagrams in UML. Message sequence charts (MSCs) are a standardized notation for asynchronously communicating processes. The norm Z.120 also includes hierarchical HMSCs. Algorithms on MSCs rarely take into account all possibilities covered by the norm. In particular, hierarchy is not taken into account since the models that are usually considered are (flat) MSC-graphs, that correspond to the unfolding of hierarchical HMSCs. However, complexity can increase exponentially by unfolding. The aim of this paper is to show that basic algorithms can be designed such that they avoid the costly unfolding of hierarchical MSCs and HMSCs. We show this for the membership and the pattern matching problem. We prove that the membership problem for hierarchical HMSCs is PSPACE-complete. Then we describe a polynomial time algorithm for the pattern matching problem on hierarchical MSCs.

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Authors and Affiliations

  1. IRISA/CNRS, Campus de Beaulieu, 35042, Rennes, France

    Blaise Genest

  2. LaBRI, Université Bordeaux, 351 cours de la Libération, 33405, Talence, France

    Anca Muscholl

Authors
  1. Blaise Genest
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  2. Anca Muscholl
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Correspondence to Anca Muscholl.

Additional information

The results were obtained while B. Genest was affiliated with LIAFA, Université Paris 7.

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Genest, B., Muscholl, A. Pattern Matching and Membership for Hierarchical Message Sequence Charts. Theory Comput Syst 42, 536–567 (2008). https://doi.org/10.1007/s00224-007-9054-1

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  • DOI: https://doi.org/10.1007/s00224-007-9054-1

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