Abstract
We define a family of graphs whose the monadic theory is linearly reducible to the monadic theory S2S of the complete deterministic binary tree. This family contains strictly the context-free graphs investigated by Muller and Schupp, and also the equational graphs defined by Courcelle. Using words for vertices, we give a complete set of representatives by prefix rewriting of rational languages. This subset is a boolean algebra preserved by transitive closure of arcs and by rational restriction on vertices.
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© 1996 Springer-Verlag Berlin Heidelberg
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Caucal, D. (1996). On infinite transition graphs having a decidable monadic theory. In: Meyer, F., Monien, B. (eds) Automata, Languages and Programming. ICALP 1996. Lecture Notes in Computer Science, vol 1099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61440-0_128
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DOI: https://doi.org/10.1007/3-540-61440-0_128
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