Abstract
We introduce probabilistic graph grammars. These are graph grammars with additional probabilities attached to the production rules. This adds a probabilistic use to the ordinary graph grammars. We describe some methods from numerical analysis to compute some statistical measures of generated graphs. We show how to determine the average size of an inductive function, or the probability of an inductive graph property.
This work has been supported by the “Programme de Recherches Coordonnées: Mathématiques et Informatique” and the ESPRIT Basic Research Action 3299 “Computing by Graph Transformations”.
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References
M. Bauderon and B. Courcelle. Graph rewriting and graph expressions. Math. Systems Theory, 20 (1987) 83–127.
T.L. Boot and R.A. Thompson. Applying probability measures to abstract languages. IEEE Trans. Comput., C-22, 5 (1973) 442–450.
B. Courcelle. An axiomatic definition of context-free rewriting and its application to NLC graph grammars. Theoret. Comput. Sci, 55 (1987) 141–181.
B. Courcelle. Graph rewriting: an algebraic and logic approach. Handbook of Computer Science, B (1990) 193–242.
B. Courcelle and M. Mosbah. Monadic second-order evaluations on tree-decomposable graphs. Report 90-110, Bordeaux-1 University (1990). To appear in TCS 92, a short version in WG'91, LNCS 570.
H. Erigh, M. Nagl, G. Rozenberg, and A. Rosenfeld, editors. Graph-Grammars and their application to Computer Science, LNCS 291, 3rd International Workshop, Warrenton, Virginia, USA, December 1986. Springer-Verlag.
H. Erigh, G. Rozenberg, and H.J. Kreowski, editors. Graph-Grammars and their application to Computer Science, LNCS 532, 4th International Workshop, Bremen, Germany, March 1990. Springer-Verlag.
W. Fellier. An introduction to probability theory and its applications, volume Vol. 1. 2nd ed. Wiley, New York (1957).
R. Godement. Cours d'algèbre, ed. Hermann (1963).
A. Habel. Hyperedge Replacement: Grammars and Languages. PhD thesis, University of Bremen (1989).
S.E. Hutchins. Moments of string and derivation lengths of stochastic context-free grammars. Inform. Sciences, 4 (1972) 179–191.
C. Lautemann. Efficient algorithms on context-free graph grammars. Acta Inform., 27 (1990) 399–421.
M. Mosbah. Algebraic And Logical Methods For The Construction Of Algorithms On Tree-Decomposable Graphs. PhD thesis, University of Bordeaux-1 (1992).
S. Sole. Entropies of probabilistic grammars. Information and Control, 25 (1974) 57–74.
C.S. Wetherell. Probabilistic languages: A review and some open questions. ACM Comput. Surv., 12, 4 (1980) 361–379.
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© 1993 Springer-Verlag Berlin Heidelberg
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Mosbah, M. (1993). Probabilistic graph grammars. In: Mayr, E.W. (eds) Graph-Theoretic Concepts in Computer Science. WG 1992. Lecture Notes in Computer Science, vol 657. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56402-0_51
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DOI: https://doi.org/10.1007/3-540-56402-0_51
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