Abstract
We study languages (i.e. sets) of planar directed acyclic graphs (pdags). These pdags are constructed by parallel composition and serial composition of letters and pdags on a doubly ranked alphabet. Our purpose is to introduce an algorithmic process (generalization of Kamimura and Slutzki's parallel automata) for accepting pdag languages and a specification of these languages by means of well-suited rational expressions. So our main result is a Kleene-like theorem proving the equivalence between rationality and automaton-definability.
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References
ARNOLD, A. and DAUCHET, M. (1978), Théorie des Magmoides (I), RAIRO Informatique Théorique 12-3, 235–257.
ARNOLD, A. and DAUCHET, M. (1979), Théorie des Magmoides (II), RAIRO Informatique Théorique 13-2, 135–154.
BOSSUT, F. and WARIN. B. (1986), "Rationalité et reconnaissabilité dans des Graphes Acycliques", Doctorat, Université de Lille I.
CLAUS, V., EHRIG, H., ROZENBERG, G. Ed. (1979), "Graph Grammars and their Applications to Computer Sciences and Biology", L.N.C.S. 73.
COURCELLE, B. (1987), Recognizability and Second-Order Definability for Sets of Finite Graphs, Technical Report no I-8634, University of Bordeaux.
COURCELLE, B. (1988), On recognizable sets and tree automata, To appear in Proceedings of the Colloquium on Resolution Equations in Algebraic Structures, Austin
DEGANO, P. and MONTANARI, V. (1985), Specification Languages for Distribued Systems, TAPSOFT'85-L.N.C.S. 185, 29–51.
EHRIG, H., PFENDER, M., SCHNEIDER, H, J., Ed. (1983), "Graph Grammars and their Applications to Computer Sciences", L.N.C.S. 153.
EILENBERG, S. and WRIGHT, J.B. (1967), Automata and tree grammars, Inf. and Control 11, 217–231.
ENGELFRIET, J. (1975), Bottom-up and Top-down tree transformations-a comparison, Math Syst Theory 9, 193–231.
GRABOWSKY, J. (1981), On Partial Languages, Fund. Informaticae 4, 427–498.
KAMIMURA, T. and SLUTZKI, G. (1981), Parallel and Two-way Automata on Directed Ordered Acyclic Graphs, Information and Control 49, 10–15.
KAMIMURA, T. and SLUTZKI, G. (1982), Transductions of Dags and Trees, Math. SysT. Theory 15, 225–249.
MARTELLI and MONTANARI, V. (1982), An Efficient Unification Algorithm, Transactions on Programming Languages and Syst., 256–282.
OCHMANSKI, E. (1985), Regular Behaviour of Concurrent Systems, Bull. EATCS 27.
THATCHER, J. W. (1973), Tree automata: Informal Survey, In Currents in the Theory of Computing (A.V, Aho, Ed.), Prentice-Hall, Englewood Cliffs, 143–172.
WINKOWSKI, J. (1979), An Algebraic Approach to Concurrence, MFCS 79-L.N.C.S. 74, 523–532.
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© 1988 Springer-Verlag Berlin Heidelberg
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Bossut, F., Dauchet, M., Warin, B. (1988). Automata and rational expressions on planar graphs. In: Chytil, M.P., Koubek, V., Janiga, L. (eds) Mathematical Foundations of Computer Science 1988. MFCS 1988. Lecture Notes in Computer Science, vol 324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017142
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DOI: https://doi.org/10.1007/BFb0017142
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