Transcript A Quantitative Completeness Analysis for Property-Sets Martin Oberkönig Martin Schickel, Hans Eveking Computer Systems Group A Quantitative Completeness Analysis for Property-Sets, November 2007

1
A Quantitative Completeness Analysis for
Property-Sets
Martin Oberkönig
Martin Schickel, Hans Eveking
Computer Systems
Group
A Quantitative Completeness Analysis for
Property-Sets, November 2007
2
Overview

Introduction

Completeness Metric

Normalization & Dependencies

Experimental Results

Conclusions
A Quantitative Completeness Analysis for
Property-Sets, November 2007
3
Motivation
how many?
Properties
A Quantitative Completeness Analysis for
Property-Sets, November 2007
4
Analysis
 Gap
 Complete
Properties
 X% complete
A Quantitative Completeness Analysis for
Property-Sets, November 2007
5
Completeness Metric
+
Example:
Consistent
example:
a
ac
b  c
1
???
c
0
b
A Quantitative Completeness Analysis for
Property-Sets, November 2007
a c
ab  c
6
Completeness Metric
+
undetermined cases
a
(a
ab
c
a  b
 b)
a c
a  b  c
determined cases
A Quantitative Completeness Analysis for
Property-Sets, November 2007
7
Completeness Metric
+
va1
degree of determination =
out
c
a vb
0
#3minterms (v0  v1 )
# determined cases
= 75 n%
=
# all cases
4
2
A Quantitative Completeness Analysis for
Property-Sets, November 2007
8
1. Problem:
 Required: Properties constraining only one single signal
 Real World: Arbitrarily written properties
property amba_address_increment is
assume:
at t:
HTRANS=cSEQ or HTRANS=cNONSEQ;
-- beat performed
at t:
isINCBURST;
-- INCR burst
at t:
HREADY='1';
-- transfer complete
prove:
at t+1:
HADDR = (PREV(HADDR) +
shift_left("00000001",HSIZE))(31 downto 0)
or HTRANS=cNONSEQ or HTRANS=cIDLE;
end property;
-- or burst finished
Solution: Normalization Algorithm
A Quantitative Completeness Analysis for
Property-Sets, November 2007
9
2. Problem:
true  a  b
ab
 a  b
ba
b  a
??????
? ?
??????
? ?
100% determination for b
Solution:
100% determination for a
 Property dependency graph
 Fixpoint iteration
A Quantitative Completeness Analysis for
Property-Sets, November 2007
10
Experimental Results (Overview)
Component
ATM Error
Controller
AMBA Slave
AMBA Master
Prop.
normal.
Prop.
Analysis
Time
5
7
0.1 s
8
497
0.69 s
20
3290
7.3 s
A Quantitative Completeness Analysis for
Property-Sets, November 2007
11
Results (Detailed)
Component
ATM Error
Controller
AMBA Slave
Signal
reject_it
correct_it
act_master(3..0)
split_master(15..0)
selected
hsplit(15..0)
hresp(1..0)
hready
hrdata(31..0)
Output /
Internal
out
out
int
int
int
out
out
out
out
A Quantitative Completeness Analysis for
Property-Sets, November 2007
Determination
100%
100%
100%
49%
100%
49%
21%
21%
0%
12
Conclusion
 Property-set analysis leading to a metric
 Full symbolic representation of the gap
 No design needed
 100% complete ≠ error-free
 Ongoing work:
 Degree of freedom
 Interpretation of the metric
A Quantitative Completeness Analysis for
Property-Sets, November 2007
13
Thanks for your
attention!
Any Questions?
A Quantitative Completeness Analysis for
Property-Sets, November 2007
14
more Results
Component
FIFO
(K. Claessen)
Component
FIFO
(K. Claessen)
Prop.
normal.
Prop.
Analysis
Time
6
120
0.26 s
Signal
err
num(1..0)
num(3..2)
first(15..0)
Output /
Internal
out
out
out
out
A Quantitative Completeness Analysis for
Property-Sets, November 2007
Determination
75%
70%
37%
46%