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By J. Hartmanis, R. Stearns,

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Extra info for Algebraic Structure Theory of Sequential Machines [appl math]

Example text

4 The p-value next to a vertex gives the probability of being occupied for that vertex. 2 (iv)). ul p(l) U A.

In view of these considerations we introduce planar * of a matching pair G and G, * as well as modifications Gp~ and Gp~ 22 planar modific~tion ~~ of a mosaic ~. 1). Let (G,G) be a matching pair based on (~,J). We then construct Gp~ as follows: Its vertex set is the vertex set of Q plus one additional vertex in each face F of J. The added vertex inside F will be called the central vertex of F. Two vertices v and w of Gp~ will be adjacent on Qp~ iff v and ware adjacent on ~, or if one of them is the central vertex of some F s J and the other is on the perimeter of the same face F.

No confusion with the occupied cluster of v on ~p£ can arise because the latter equals Wp£ (v). 16), an occupi ed path on ~£ cannot contain any central vertices of Gp£' and therefore is an occupied path on Gp£ itself. 1 therefore has the following corollary. 1. 20) Wp£(v) For any vertex v of G W(v) U {all edges of Gp£ from a central vertex of Gp£ to some vertex w E W(v)}. ::. /I. for some WE W}. lb, respectively. Thus the non-central vertices of Wo£ are precisely the vertices of W. 20). 0 Remark.

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Algebraic Structure Theory of Sequential Machines [appl math] by J. Hartmanis, R. Stearns,

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