Download E-books Modeling in Event-B: System and Software Engineering PDF

By Jean-Raymond Abrial

A pragmatic textual content compatible for an introductory or complex path in formal equipment, this publication provides a mathematical method of modelling and designing platforms utilizing an extension of the B formal process: Event-B. according to the assumption of refinement, the author's systematic process permits the consumer to build types progressively and to facilitate a scientific reasoning procedure through proofs. Readers will easy methods to construct types of courses and, extra often, discrete platforms, yet this can be all performed with perform in brain. the varied examples supplied come up from numerous resources of desktop method advancements, together with sequential courses, concurrent courses and digital circuits. The ebook additionally features a huge variety of workouts and initiatives ranging in trouble. all of the examples incorporated within the e-book has been proved utilizing the Rodin Platform device set, that's on hand loose for obtain at

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Three. 17. strongly synchronized action-reactions we wish now to synchronize those activities and reactions in order that the second one response, s, purely happens while the first one, r, is enabled. In different phrases, we want to make sure the subsequent: s = 1 ⇒ r = 1. r =1 s=1 => r=1 s=1 Fig. three. 18. Synchronizing strongly synchronized action–reactions this is often illustrated in Fig. three. 18, the place the dashed arrows point out this new synchronization. yet this synchronization among the 2 is meant to be vulnerable in simple terms. For 3. eight one other layout trend: susceptible synchronization of 2 robust reactions 129 Motor could be began and stopped numerous instances grab is disengaged Motor is operating snatch could be disengaged and re-engaged numerous occasions Fig. three. 19. vulnerable synchronization of the motor and the grasp instance, in our case, it really is attainable that the motor is began and stopped a number of instances earlier than the snatch is certainly engaged. Likewise, it truly is attainable that the grasp is disengaged and re-engaged numerous occasions prior to the motor is stopped. All that's illustrated in Fig. three. 19. In Fig. three. 19, the hot courting among a number of the occasions is illustrated through the dashed arrows. reasons why those arrows are dashed is that we've got an extra constraint declaring that we don't are looking to alter the reacting occasions s_on and r_off. this can be illustrated in Fig. three. 20. extra accurately, we wish to act on the point of the activities that have enabled those occasions. this is often what we will formalize within the subsequent part. three. eight. 2 Modeling subsequent is a blind reproduction of the 2 strongly synchronized styles: dbl0_1: dbl0_2: dbl0_3: dbl0_4: dbl0_5: dbl0_6: a ∈ {0, 1} r ∈ {0, 1} ca ∈ N cr ∈ N a = 1 ∧ r = zero ⇒ ca = cr + 1 a = zero ∨ r = 1 ⇒ ca = cr dbl0_7: dbl0_8: dbl0_9: dbl0_10: dbl0_11: dbl0_12: b ∈ {0, 1} s ∈ {0, 1} cb ∈ N cs ∈ N b = 1 ∧ s = zero ⇒ cb = cs + 1 b = zero ∨ s = 1 ⇒ cb = cs 130 A mechanical press controller a_on a_off r_on r_off b_on b_off s_on s_off Fig. three. 20. susceptible synchronization of 2 strongly synchronized action–reactions a_on while a=0 r=0 then a, ca := 1, ca + 1 finish a_off whilst a=1 r=1 then a := zero finish r_on while r=0 a=1 then r, cr := 1, cr + 1 finish r_off whilst r=1 a=0 then r := zero finish b_on while b=0 s=0 then b, cb := 1, cb + 1 finish b_off while b=1 s=1 then b := zero finish s_on whilst s=0 b=1 then s, cs := 1, cs + 1 finish s_off while s=1 b=0 then s := zero finish We now refine those styles via introducing our new requirement: dbl1_1: s = 1 ⇒ r = 1 3. eight one other layout trend: susceptible synchronization of 2 powerful reactions 131 the one occasions that would reason an issue in proving this invariant are s_on (setting s to at least one) and r_off (setting r to 0). to be able to remedy this challenge, it kind of feels sufficient so as to add the guards r = 1 and s = zero to occasions s_on and r_off respectively: s_on while s=0 b=1 r=1 then s, cs := 1, cs + 1 finish r_off whilst r=1 a=0 s=0 then r := zero finish yet, as indicated above, we don't are looking to contact those reacting occasions. that allows you to receive an identical effect, it really is sufficient so as to add the subsequent invariants: dbl1_2: b = 1 ⇒ r = 1 dbl1_3: a = zero ⇒ s = zero in an effort to keep invariant dbl1_2, we need to adjust occasion b_on by way of including the defend r = 1 to it because it units b to one: b_on while b=0 s=0 then b := 1 cb := cb + 1 finish ❀ b_on whilst b=0 s=0 r=1 then b := 1 cb := cb + 1 finish 132 A mechanical press controller to keep up invariant dbl1_2, we now have additionally so as to add the protect b = zero to occasion r_off because it units r to zero: r_off while r=1 a=0 then r := zero finish ❀ r_off whilst r=1 a=0 b=0 then r := zero finish yet, back, we don't are looking to contact this reacting occasion, so we introduce the subsequent invariant: dbl1_4: a = zero ⇒ b = zero to be able to preserve invariant dbl1_3: that's: dbl1_3: a = zero ⇒ s = zero , we need to refine occasion a_off as follows (guard strengthening): a_off while a=1 r=1 then a := zero finish ❀ a_off whilst a=1 r=1 s=0 then a := zero finish 3.

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