CS 267 – Spring 2011 – Homework Assignment 2
Due Friday, April 29th
Do not discuss the problems with anyone other than the instructor.
1.
Write the following CTL
∗
formulas using fixpoints: AFAG
p
,
p
EU(AG
q
), EGF
p
, EFG
p
.
2.
Consider the following transition system
M
= (
AP, S, R, S
0
, L
) with the set of states
S
=
{
0
,
1
,
2
,
3
}
, the initial set of states
S
0
=
{
0
}
, the transition relation
R
=
{
(0
,
1)
,
(1
,
2)
,
(2
,
3)
,
(1
,
0)
,
(3
,
3)
}
, the set of atomic propositions
AP
=
{
p, q
}
and the labeling function
L
:
S
→
2
AP
where
L
(0) =
{
p
}
,
L
(1) =
{
q
}
,
L
(2) =
{
p
}
, and
L
(3) =
{
p, q
}
.
Based on the above transition system, show the iterative fixpoint computations (show the
set of states for each iteration) and the results for the following
μ
-calculus formulas:
νz .
(
p
∧
EX
z
))
μz .
(
q
∨
(
p
∧
AX
z
))
μy . νz .
((
q
∧
EX
z
)
∨
EX
y
)
3.
Consider the following transition system
M
= (
AP, S, R, S
0
, L
) with the set of states
S
=
{
0
,
1
,
2
,
3
}
, the initial set of states
S
0
=
{
0
}
, the transition relation
R
=
{
(0
,
1)
,
(0
,
2)
,
(1
,
3)
,
(2
,
3)
,
(3
,
3)
}
and the set of atomic propositions
AP
=
{
p
}
and the labeling function
L
:
S
→
2
AP
where
L
(0) =
∅
,
L
(1) =
∅
,
L
(2) =
∅
,
L