The Temporal Logic of Reactive and Concurrent Systems: by Zohar Manna, Amir Pnueli

By Zohar Manna, Amir Pnueli

Reactive platforms are computing platforms that are interactive, corresponding to real-time structures, working structures, concurrent structures, regulate platforms, and so on. they're one of the so much tough computing structures to software. Temporal common sense is a proper tool/language which yields first-class ends up in specifying reactive platforms. This quantity, the 1st of 2, subtitled Specification, has a self-contained advent to temporal good judgment and, extra very important, an creation to the computational version for reactive courses, built by way of Zohar Manna and Amir Pnueli of Stanford collage and the Weizmann Institute of technology, Israel, respectively.

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P[81] for every program context P[S]. Thus x Note that 82 = await x does not implement 81 = [await x] or [await y]. To see this, consider the program context P[ 8] given by: F, Y = T] local x, y: boolean where x = [ out z: integer where z = 0 8j z:= 1 Program P[81] generates the reduced behavior (listing values of z) (0), (1), (1), ... , while program P[82] generates the reduced behavior (0), (0), .... Therefore, 82 does not implement 81. 7 Grouped Statements The definition of the semantics of the text language established a set of transitions associated with each statement.

Then the transition relation for the product 7"1 0 7'2 is given by PTJ. 0T2 = PTJ. fi] 1\ (y' = e2 [eI/fiD . We use the notation c,o[eI/fi] to denote the formula c,o in which we replace every free occurrence of Yi with ei , i = 1, ... , k, where e1 = (e1, ... , e k ). : (x> y) 1\ (x' = x - y) 1\ (Y' = y) PT2: (xy) 1\ (x y) 1\ (x - Y < y) 1\ (x' =x - (y < x < 2· y) 1\ y) (y' =Y- =x - y) 1\ (x' 1\ This shows that 7'1 and 72 can be taken in succession only if y when taken they change x to x - y, and change y to 2· y - x.

Or 8 m l are given by trans (8) = trans(8t} U ... U trans (8m ). Thus, the statement 8 inherits its transitions from all of its children. • Block The transitions associated with the block statement 8 = [declaration; 8] are given by trans (8) = trans (S). Thus, the statement 8 inherits its transitions from its only child. Chapter 1: Basic Models 38 The Initial Condition Consider a program Let

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