Abstract.
The study of infinite graphs has potential applications in the specification and verification of infinite systems and in the transformation of such systems. Prefix-recognizable graphs and regular graphs are of particular interest in this area since their monadic second-order theories are decidable. Although the latter form a proper subclass of the former, no characterization of regular graphs within the class of prefix-recognizable ones has been known, except for a graph-theoretic one in [2]. We provide here three such new characterizations. In particular, a decidable, language-theoretic, necessary and sufficient condition for the regularity of any prefix-recognizable graph is established. Our proofs yield a construction of a deterministic hyperedge-replacement grammar for any prefix-recognizable graph that is regular.
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Received July 19, 1999, and in revised form December 22, 2000, and in final form March 28, 2001. Online publication July 20, 2001.
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Caucal, D., Knapik, T. An Internal Presentation of Regular Graphs by Prefix-Recognizable Graphs. Theory Comput. Systems 34, 299–336 (2001). https://doi.org/10.1007/s00224-001-1015-5
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DOI: https://doi.org/10.1007/s00224-001-1015-5