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cs-486:homework-7 [2017/02/21 17:58]
egm created
cs-486:homework-7 [2018/11/02 22:21] (current)
egm [Problems]
Line 2: Line 2:
 * Write temporal logic properties * Write temporal logic properties
 * Master the semantics of temporal logic * Master the semantics of temporal logic
 +
 +== Problems ==
 +
 +'''​1. (12 points)'''​ For the transition system, which states satisfy the formulas. L(s1) = {a}. L(s2) = {a}. L(s3) = {a,b}. L(s4) = {b}. s1 -> s2. s2 -> s3. s3 -> s1. s4 -> s2. s3 and s4 are initial states.  ​
 +* A(X a)
 +* A(XXX a)
 +* A([] b)
 +* A([]<>​a)
 +* A([](b U a))
 +* A(<>​(b U a))
 +Hint: consider each state as the starting state for the formula.
 +
 +'''​2. (16 points)'''​ This problem is Exercise 5.5 in [http://​is.ifmo.ru/​books/​_principles_of_model_checking.pdf Principles of Model Checking ] (page 321 of the PDF document), consider an elevator system that services N > 0 floors numbered 0 through N-1. There is an elevator door at each floor with a call-button and an indicator light that signals whether or not the elevator has been called. For simplicity, consider N=4. Present a set of atomic propositions-try to minimize that set-that are needed to describe the following properties of the elevator as LTL formulae and give the LTL formulae:
 +* Any door on any floor is never open when the elevator is not present
 +* A requested floor will be served eventually
 +* The elevator repeatedly returns to floor 0
 +* When the top floor is requested, the elevator serves it immediately and does not stop on any floor on the way up
 +
 +'''​3.'''​ ('''​16 points'''​) For each of the following properties: label as either safety or liveness, express in a CTL* formula, and create a minimal label trace to satisfy written formula.
 + 
 +* The number of items in a buffer may not exceed ''​n''​
 +* If a process reaches a location ''​li''​ just before a critical section, it should not be blocked forever
 +* Clients may not retain resources forever
 +* It is always cloudy before it rains
 +
 +'''​4.'''​ ('''​4 points'''​) Express the following property in LTL (the '​!'​ operator is a logical not):
 +
 +''​the transition from !p to p will happen at most once''​
 +
 +'''​5.'''​ ('''​4 points'''​) Express the following property in LTL:
 +
 +''​there are infinitely many transitions from !p to p (and vice versa)''​
 +
 +'''​6.'''​ ('''​8 points'''​) Express the following property in LTL using ''​r'',​ ''​y'',​ ''​g''​ as atomic propositions denoting the states of the traffic light (r = red, y = yellow, g = green):
 +
 +''​The lights of a traffic signal light in the following periodic sequence: red, yellow, green, red, yellow, green,... and only one light is on at any given time, starting with red. You cannot make any assumptions on how long a light is on other than it will be on for a finite length of time.''​
 +
 +'''​7.'''​ ('''​5 points'''​) Express the following property in LTL:
 +
 +''​if q holds in a state si and r holds in some subsequent state (sj , j > i) then p must not hold in any state sk in between si and sj (i < k < j , where j is the first such subsequent state)''​
 +
  
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