Abstract
A natural way to describe a family of languages is to use rational transformations from a generator. From these transformations, Ginsburg and Greibach have defined the Abstract Family of Languages (AFL). Infinite graphs (also called infinite automata) are natural tools to study languages. In this paper, we study families of infinite graphs that are described from generators by transformations preserving the decidability of monadic second order logic. We define the Abstract Family of Graphs (AFG). We show that traces of AFG are rational cones and traces of AFG that admit a rationally colored generator are AFL. We generalize some properties of prefix recognizable graphs to AFG. We apply these tools and the notion of geometrical complexity to study subfamilies of prefix recognizable graphs.
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References
J.-M. Auteber and L. Boasson. Transductions Rationnelles — Application aux Langages Algébriques. Masson, Paris, 1988.
J. Berstel. Transductions and Context-Free-Languages. B.G. Teubner, Stuttgart, 1979.
A. Blumensath. Prefix-recognizable graphs and monadic second order logic. Technical Report AIB-06-2001, RWTH Aachen, April 2001.
D. Caucal. On infinite transition graphs having a decidable monadic theory. In ICALP 1996, volume 1099 of LNCS, pages 194–205, 1996.
D. Caucal. On the transition graphs of Turing machines. In MCU 2001, LNCS, pages 177–189, 2001.
N. Chomsky and MP. Schützenberger. The algebraic theory of context-free languages in computer programming and formal systems. North Holland, 1963.
B. Courcelle. The monadic second-order logic of graphs ii: infinite graphs of bounded tree width. Math. Systems Theory, 21:187–221, 1989.
B. Courcelle. Monadic-second order definable graph transductions: a survey. TCS, vol. 126:pp. 53–75, 1994.
S. Ginsburg. Algebraic and Automata-Theoretic Properties of Formal Languages. North Holland/American Elsevier, 1975.
S. Ginsburg and S. Greibach. Abstract families of languages. Mem. Am. Math. Soc., 87, 1969.
A. Maignan. Sur la complexité des graphes réguliers. rapport de DEA (IFSIC), Rennes, 1994.
C. Morvan. Les graphes rationnels. Thèse de doctorat, Université de Rennes 1, Novembre 2001.
C. Morvan and C. Stirling. Rational graphs traces context-sensitive languages. In MFCS 2001, number 2136 in LNCS, pages 436–446, 2001.
D. Muller and P. Schupp. The theory of ends, pushdown automata, and secondorder logic. TCS, 37:51–75, 1985.
C. Rispal. Graphes rationnels synchronisés. Rapport de DEA, Université de Rennes 1, 2001.
W. Thomas. A short introduction to infinite automata. In Proceedings of the 5th international conference Developments in Language Theory, volume 2295, pages 130–144. LNCS, 2001.
T. Urvoy. Regularity of congruential graphs. In MFCS 2000, volume 1893 of LNCS, pages 680–689, 2000.
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Urvoy, T. (2003). Abstract Families of Graphs. In: Ito, M., Toyama, M. (eds) Developments in Language Theory. DLT 2002. Lecture Notes in Computer Science, vol 2450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45005-X_34
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DOI: https://doi.org/10.1007/3-540-45005-X_34
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