Concurrency of manipulations in multidimensional information structures

  • Hartmut Ehrig
  • Barry K. Rosen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 64)


Given a sequence of manipulation rules together with dependence relations (allowing later rules to depend on the effects of earlier rules), we construct a single "concurrent manipulation rule" with the following property: Each application of the sequence of rules to a multidimensional information structure — such that the dependence relations are respected — can be performed in a single step applying the concurrent manipulation rule to the same structure. Moreover this becomes a bijective correspondence between such manipulation sequences and "concurrent manipulations". This "Concurrency Theorem" is formulated and proved in the framework of the algebraic theory of graph grammars using new pushout and pullback lemmas for the 3- and 4-dimensional cube. As corollaries we obtain a recently published Church-Rosser-Theorem for graph derivations and a theorem reducing the strong to the weak Church-Rosser-property.

Key Words

Concurrency Multidimensional Information Structures Graph Grammars Parallelism Church-Rosser-Properties Applications of Category Theory 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Hartmut Ehrig
    • 1
  • Barry K. Rosen
    • 2
  1. 1.Fachbereich InformatikTechnische Universität BerlinBerlin 10Germany
  2. 2.Computer Science Dept.IBM Research CenterYorktown HeightsU.S.A.

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