Download PDF by Kai-Uwe Sattler: Algorithmen und Datenstrukturen

By Kai-Uwe Sattler

ISBN-10: 3898643859

ISBN-13: 9783898643856

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We will now show that such situations are avoidable by means of equivalent transformations of C/ E-systems. To do this, we add to each condition b its complement b, such that in every case either b or b holds. (a) Definition. Let I be a C/ E-system and let b, b' E BE. (i) b' is called the complement of b iff·b = b'· and b· = ·b' . (ii) I is called complete iff each condition b E BE has a complement b' (b) Lemma. Let I be a C / E-system and let b E BE. (i) b has at most one complement. It will be denoted by b.

P: K -4 E is an elementary process iff there is an arc v = (c], G, C2) in CPr such that p (OK) =c], P (KO) = C2, and p (TK) = G. Proof Ifp:K-4E is elementary thenp(°K) [P(TK)p(K O) is a step in E, so (p (0 K),p (h), P (KO)) is an arc in CPr. Conversely, if (c], G, C2) is any arc in CPr then c] [G) C2. Let K= (c] U C2, G; Fr n (c] U C2 U G)2); then id: K -4 E is an elementary process of E. 0 This lemma establishes a unique correspondence between elementary processes and arcs, and we therefore define: 42 Processes of Condition IEvent-Systems {I,'} y~ )"S} p= {o c} U,4} /' \o\.

For example, the net of the four seasons in Fig. ) Such a set of cases C should have the following properties: 22 Nets Consisting of Conditions and Events 1) If a step G s; E is possible in a case C E C, then G leads again to a case in C (steps do not lead out of C). 2) Conversely, if a case C E C can result from a step G s; E, then the situation we moved from was also a case of C. (In other words, when we reason backwards and look for preceding cases, we only find cases of C). 3) All cases in C can (by forward and backward reasoning) be transformed into each other.

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Algorithmen und Datenstrukturen by Kai-Uwe Sattler


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