Abstract
Since Muller and Schupp have shown that monadic second-order logic is decidable for context-free graphs in [MS85], several specialized procedures have been developed for related problems, mostly for sublogics like the modal μ-calculus, or even its alternation-free fragment. This work shows the decidability of SlS, the trace version of MSOL, for the richer set of macro graphs. The generation mechanism of macro graphs is of higher-order nature and relates to the context-free one like macro grammars [Fis68] relate to context-free grammars.
Technically, the result follows from the decidability of the emptiness problem of the trace language of a macro graph with fairness. The decision procedure is given in form of a tableau system. Soundness and completeness follow from the relation of the (finite) tableaux to their infinite unfoldings. This kind of proof promises to be helpful in the derivation of further results.
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Hungar, H. (1999). Model Checking and Higher-Order Recursion. In: Kutyłowski, M., Pacholski, L., Wierzbicki, T. (eds) Mathematical Foundations of Computer Science 1999. MFCS 1999. Lecture Notes in Computer Science, vol 1672. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48340-3_14
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DOI: https://doi.org/10.1007/3-540-48340-3_14
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