CS 267 – Spring 2011 – Homework Assignment 3
Due Friday, May 20th
Do not discuss the problems with anyone other than the instructor.
1.
Give a B¨uchi automaton that corresponds to the LTL property
GFp
.
Given the transition system
T
= (
S,I,R
) where
I
=
{
0
}
,
S
=
{
0
,
1
,
2
}
and
R
=
{
(0
,
0)
,
(0
,
1)
,
(1
,
2)
,
(2
,
1)
,
}
, assume that the only state which satisfies the atomic proposition
p
is 1. Show the
B¨uchi automaton
A
T
that corresponds to this transition system (based on the construction given
in the lecture notes), and the product automaton
A
T
×
A
f
.
If there is one, show an accepting run of the product automaton and show the path in the transition
system
T
which corresponds to this run and satisfies the LTL formula
GFp
.
Does the transition system
T
satisfy the property
FG
¬
p
? Why?
2.
Construct a B¨uchi automaton that corresponds to the LTL property
p U
(
q
∧
X p
) using the
LTLB¨uchi automata translation algorithm. Show the intermediate steps (like the example in the
lecture notes).
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 Fall '09
 bultan
 Dining philosophers problem, Sleeping barber problem, SPIN model checker, B¨chi automaton, reachable state space

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