Abstract
Graph language recognizability is defined and investigated by virtue of the syntactic magmoid, analogously with the syntactic monoid of a word language. In this setup, the syntax complexity of a given recognizable graph language can be determined, giving rise to a syntactic classification inside the class of recognizable graph languages.
Similar content being viewed by others
References
Arnold, A., Dauchet, M.: Théorie des magmoides. I. RAIRO Inform. Théor. 12(3), 235–257 (1978)
Arnold, A., Dauchet, M.: Théorie des magmoides. II. RAIRO Inform. Théor. 13(2), 135–154 (1979)
Bauderon, M., Courcelle, B.: Graph expressions and graph rewritings. Math. Syst. Theory 20, 83–127 (1987)
Bossut, F., Dauchet, M., Warin, B.: A Kleene theorem for a class of planar acyclic graphs. Inform. and Comput. 117, 251–265 (1995)
Bell, E.T.: Exponential numbers. Amer. Math. Monthly 41, 411–419 (1934)
Benson, D.B.: The basic algebraic structures in categories of derivations. Inform. and Control 28, 1–29 (1975)
Bozapalidis, S., Kalampakas, A.: An axiomatization of graphs. Acta Informatica 41, 19–61 (2004)
Corradini, A., Gadducci, F.: An algebraic presentation of term graphs, via gs-monoidal categories. Appl. Categ. Structures 7(4), 299–331 (1999)
Courcelle, B.: The monadic second-order logic of graphs. I. Recognizable sets of finite graphs. Inform. and Comput. 85, 12–75 (1990)
Eilenberg, S.: Automata, Languages and Machines, vol. A. Academic Press (1974)
Engelfriet, J., Vereijken, J.J.: Context-free graph grammars and concatenation of graphs. Acta Informatica 34, 773–803 (1997)
Engelfriet, J., Schmidt, E.M.: IO and OI I. J. Comput. Syst. Sci. 15(3), 328–353 (1977)
Gadducci, F., Heckel, R.: An inductive view of graph transformation. Recent Trends in Algebraic Development Techniques (Tarquinia 1997), pp. 223–237. Lecture Notes in Computer Science 1376, Springer (1997)
Gibbons, J.: An initial-algebra approach to directed acyclic graphs. Mathematics of program construction (Kloster Irsee, 1995), pp. 282–303. LNCS 947, Springer, Berlin (1995)
Hotz, G.: Eine Algebraisierung des Syntheseproblems von Schaltkreisen. EIK 1, pp. 185–205, 209–231 (1965)
Hotz, G.: Eindeutigkeit und Mehrdeutigkeit formaler Sprachen. EIK 2, 235–246 (1966)
Kamimura, T., Slutzki, G.: Parallel and two-way automata on directed ordered acyclic graphs. Inform. and Control 49, 10–51 (1981)
MacLane, S.: Categories for the Working Mathematician. Springer Verlag (1971)
Mezei, J., Wright, J.: Algebraic automata and context-free sets. Inform. and Control 11, 3–29 (1967)
Perrin, D.: (Chapter 1) Finite Auomata. Handbook of Theoretical Computer Science. In: van Leeuwen, J. (ed.), Vol. B, MIT Press (1990)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bozapalidis, S., Kalampakas, A. Recognizability of graph and pattern languages. Acta Informatica 42, 553–581 (2006). https://doi.org/10.1007/s00236-006-0006-z
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00236-006-0006-z