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2. Support information reference:
3. These Operations Specifications are approved by direction of the Administrator.
DIGITALLY FAA SIGNED 10/30/2007 1:25:25 PM
Tate, Douglas W.
Principal Maintenance Inspector
4. Date Approval is effective: 10/30/2007 Amendment Number: 2
DIGITALLY INDUSTRY SIGNED 10/30/2007 1:15:38 PM
5. I hereby accept and receive the Operations Specifications in this paragraph.
Mayer, Stan
FAA Accountable Manager, 145 Date: 10/30/2007
Print Date: 11/12/2007 A449-2 Certificate No.: I6XR049Y
AAR Aircraft Services Inc.
U.S. Department
of Transportation
Federal Aviation Operations Specifications
Administration
D100. Work to be Performed at a Place Other Than the HQ Control: 11/16/04
Repair Station Fixed Location(s) HQ Revision: 050
a. The certificate holder may perform work at a place other than its Fixed Location (as listed in
paragraph A001, and paragraph A101 if issued, of these operations specifications) provided it has the
facilities, material, equipment and technical personnel to perform the work authorized in the following
table.
Table 1
Work Authorized Repair Stations Manual
References
Quality Control Manual
References
As per paragraph A003 Repair Station Manual Section 7 NONE
b. The certificate holder may not perform continuous operation at a facility other than the station’s
Fixed Location listed in paragraph A001, and paragraph A101 if issued.
c. Line Stations. Privileges of a line station, as set forth by the EASA certificate and scope of work and
located within the country where the main facility is domiciled are listed in Table 1 are authorized.
d. Work may be due to a special circumstance or on a recurring basis. If on a recurring basis, the repair
station must have procedures in its manual.
1. The Certificate Holder applies for the Operations in this paragraph.
2. Support information reference:
3. These Operations Specifications are approved by direction of the Administrator.
DIGITALLY FAA SIGNED 10/30/2007 1:23:42 PM
Tate, Douglas W.
Principal Maintenance Inspector
4. Date Approval is effective: 10/30/2007 Amendment Number: 2
DIGITALLY INDUSTRY SIGNED 10/30/2007 1:19:30 PM
5. I hereby accept and receive the Operations Specifications in this paragraph.
Mayer, Stan
FAA Accountable Manager, 145 Date: 10/30/2007
Print Date: 11/12/2007 D100-1 Certificate No.: I6XR049Y
AAR Aircraft Services Inc.
1
Abstract Interpretation
and
Predicate Abstraction
2
Automating Verification of Software
• Remains a “grand challenge” of computer
science
• Behavioral abstraction is central to this
effort
– abstractions simplify our view of program
behavior
– proofs over the abstractions carry over to
proofs over the program
3
unreachable
States
Reachability
reachable
init
unsafe
unsafe
4
Safe Invariants
• Q is a safe invariant if
– init  Q
– T(Q)  Q
– Q  safe
T(Q)
init
Q
unsafe
5
Abstraction =
Overapproximation of Behavior
T(Q)
init
Q
unsafe
Q#
T#(Q#)
6
Unlocked Locked
Error
Rel Acq
Acq
Rel
do {
KeAcquireSpinLock();
nPacketsOld = nPackets;
if(request){
request = request->Next;
KeReleaseSpinLock();
nPackets++;
}
} while (nPackets != nPacketsOld);
KeReleaseSpinLock();
More Concretely
7
s:=U;
do {
assert(s=U); s:=L;
if(*){
assert(s=L); s:=U;
}
} while (*);
assert(s=L); s:=U;
Abstraction (via Boolean program)
do {
KeAcquireSpinLock();
nPacketsOld = nPackets;
if(request){
request = request->Next;
KeReleaseSpinLock();
nPackets++;
}
} while(nPackets!=nPacketsOld);
KeReleaseSpinLock();
8
s:=U;
do {
assert(s=U); s:=L;
if(*){
assert(s=L); s:=U;
}
} while (*);
assert(s=L); s:=U;
Abstraction (via Boolean program)
U
L
L
L
L
U
L
U
U
U
E
L
E
9
Overapproximation Too Large!
init
Q
unsafe
Q#
10
Refined Boolean Abstraction
s:=U;
do {
assert(s=U); s:=L;
b := true;
if(*){
assert(s=L); s:=U;
b := b ? false : *;
}
} while ( !b );
assert(s=L); s:=U;
b : (nPacketsOld == nPackets)
do {
KeAcquireSpinLock();
　
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