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Extra resources for Theoretical Computer Science, Volume 281, Issues 1-2, Pages 1-630 (3 June 2002), Selected Papers in Honour of Maurice Nivat

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7] A. Bergeron, A uniÿed approach to control problems in discrete event processes, RAIRO-Inform. ThÃeor. 27 (1993) 555–573. [8] L. Boasson, M. Nivat, Centers of languages, in: Proceedings of the Fifth GI Conference in Computer Science, Lecture Notes on Computer Science, Vol. 104, 1981, pp. 245 –251. [9] A. Dicky, An algebraic and algorithmic method of analyzing transition systems, Theoret. Comput. Sci. 46 (1986) 285–303. R. Hoare, Communicating sequential processes, Commun. ACM 21 (1978) 666–677.

Bottom: the three real branches of the characteristic curve, one large of order z −1=3 , and two small of order ±z 1=2 (two complex branches of order e±2i =3 z −1=3 are not shown). 1. Walks and bridges We start with the easy case of unconstrained walks and bridges. This already makes use of the characteristic curve and some of its branches. Theorem 1. The bivariate generating function (BGF) of paths (with z marking size and u marking ÿnal altitude) relative to a simple set of steps S with characteristic polynomial P(u) is a rational function.

A bridge is a path whose end-point Pn lies on the x-axis. A meander is a path that lies in the quarter plane Z¿0 × Z¿0 . An excursion is a path that is at the same time a meander and a bridge; it thus connects the origin to a point lying on the x-axis and involves no point with negative y-coordinate. A family of paths is said to be simple if each allowed step in S (Deÿnition 1) is of the form (1; b) with b ∈ Z. In this case, we also abbreviate S as S= {b1 ; : : : ; bm }. In the simple case the size of a path coincides with its span along the horizontal direction, that is, its length.

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Theoretical Computer Science, Volume 281, Issues 1-2, Pages 1-630 (3 June 2002), Selected Papers in Honour of Maurice Nivat by P.-L. Curien (ed.)


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