Abstract
We give examples to show that not even c-edNCE, the most general known notion of context-free graph grammar, is suited for the specification of some common data structures.
To overcome this problem, we use monadic second-order logic and introduce edge constraints as a new means of specifying a large class of graph families. Our notion stems from a natural dichotomy found in programming practice between ordinary pointers forming spanning trees and auxiliary pointers cutting across.
Our main result is that for certain transformations of graphs definable in monadic second-order logic, the question of whether a graph family given by a specification A is mapped to a family given by a specification B is decidable. Thus a decidable Hoare logic arises.
The author is supported by a fellowship from the Danish Research Council.
The author is partially supported by the BRICS Center under the Danish Research Foundation.
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© 1994 Springer-Verlag Berlin Heidelberg
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Klarlund, N., Schwartzbach, M.I. (1994). Graphs and decidable transductions based on edge constraints. In: Tison, S. (eds) Trees in Algebra and Programming — CAAP'94. CAAP 1994. Lecture Notes in Computer Science, vol 787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017482
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DOI: https://doi.org/10.1007/BFb0017482
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