Example Y is the orthogonal Being in Y entails product of A and D being in some combination of B Y or C with E,F,or G that is AYD default (inG Entering Y by defaulting is actually entering the G combination(B,F)by the default arrows Tian Zhang Nanjing University 16
Tian Zhang @ Nanjing University 16 Example Being in Y entails being in some combination of B or C with E, F, or G that is A X D Entering Y by defaulting is actually entering the combination (B, F) by the default arrows default Y is the orthogonal product of A and D
Example (2) Conventional AND-free equivalent This is root of the exponential blow- up in the number B,F 8 of states B,E B,G 1 C,E C,G AND is Syntax sugar? C,F 8 Tian Zhang Nanjing University 17
Tian Zhang @ Nanjing University 17 Example (2) Conventional AND-free equivalent This is root of the exponential blowup in the number of states AND is Syntax sugar?
Dependency in Independency Formally,orthogonal product is a generalization of the usual product of automata the difference is that the latter is usually required to be a disjoint product,whereas here some dependence between components can be introduced 0 show dependence by common events or conditions Tian Zhang Nanjing University 18
Tian Zhang @ Nanjing University 18 Dependency in Independency Formally, orthogonal product is a generalization of the usual product of automata the difference is that the latter is usually required to be a disjoint product, whereas here some dependence between components can be introduced show dependence by common events or conditions
“inG”-like Condition orthogonal product A (inG B,F 8 B,E B,G Y R usual product of automata C,E C,G C,F 8 Tian Zhang Nanjing University 19
Tian Zhang @ Nanjing University 19 “in G”- like Condition orthogonal product usual product of automata
Broadcast-Communication Broadcast-communication实际上是orthogonality所需 要的一种产物 (A,C,E) E entered B) a(in A) F Tian Zhang Nanjing University 20
Tian Zhang @ Nanjing University 20 Broadcast-Communication Broadcast-communication实际上是orthogonality所需 要的一种产物 (A, C, E)