A Truly Concurrent Semantics for the \(\mathbb{K}\) Framework Based on Graph Transformations

  • Traian Florin Şerbănuţă
  • Grigore Roşu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7562)


This paper gives a truly concurrent semantics with sharing of resources for the \(\mathbb{K}\) semantic framework, an executable (term-)rewriting-based formalism for defining programming languages and calculi. Akin to graph rewriting rules, the \(\mathbb{K}\) (rewrite) rules explicitly state what can be concurrently shared with other rules. The desired true concurrency is obtained by translating the \(\mathbb{K}\) rules into a novel instance of term-graph rewriting with explicit sharing, and then using classical concurrency results from the double-pushout (DPO) approach to graph rewriting. The resulting parallel term-rewriting relation is proved sound, complete, and serializable with respect to the jungle rewriting flavor of term-graph rewriting, and, therefore, also to term rewriting.


Graph Transformation Variable Node Graph Grammar Semantic Framework Operation Node 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Traian Florin Şerbănuţă
    • 1
    • 2
  • Grigore Roşu
    • 1
    • 2
  1. 1.Alexandru Ioan Cuza University of IaşiRomania
  2. 2.University of Illinois at Urbana-ChampaignUSA

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