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- C event : the cost incurred to handle each critical event (i.e., in TT mode, this
includes the costs of writing and retrieving the history, and the property
evaluation; in ET mode, this includes calling the monitor and the property
evaluation),
- C switch : the cost incurred from switching between ET and TT modes and
vice versa, and
- C sample : the cost incurred from sampling in TT mode.
To derive expressions for the monitoring overhead, the cost of monitoring is
broken down into five elementary cost values, which capture the costs incurred
from performing specific interactions between the program and the monitor:
- c ET : cost of invoking monitor to check a single critical event in ET mode
- c hist : cost of saving a critical event into the history buffer in TT mode
- c TT : cost of processing the history buffer at a sample in TT mode
- c E→T : cost of a switch from ET mode to TT mode
- c T→E : cost of a switch from TT mode to ET mode
Note that these costs are derived in terms of best-case execution time of the
corresponding instructions. In particular, we calculate these costs in the same
fashion we obtain the arc weights of a control-flow graph (see Definition 1).
3.2 Problem Definition
V,v 0 ,A,w,v f
Let G =
V
be the set of critical vertices after computing the longest sampling period LSP
through application of 3 steps given in Section 2. We are also given five el-
ementary costs c ET ,c hist ,c TT ,c E→T , and c T→E as defined in Subsection 3.1.
Assuming all execution paths in G are equally likely, our goal is to find a HyRV
monitoring scheme M , such that M o ( G ) (monitoring overhead of M ) is mini-
mum. A HyRV monitoring scheme is
be the control-flow graph of program P and V c
M : V
→{
0 , 1
}
(1)
Where 0 denotes that vertex should be monitored using ET monitor whereas
1 indicates TT monitor should be used to monitor the vertex. Note that to
uniquely determine the location of a switch, we take domain of V rather than
just V c .Foragivenpath π = v 0
v f of G , the overhead of a
v 1 → ··· →
monitoring scheme is defined as:
M o ( π )=
v
[ c ET ·
(1
M ( v )) + c hist ·
M ( v )]
V c
+
( v 1 ,v 2 ) ∈A
[ c E→T ·
(1
M ( v 1 ))
·
M ( v 2 )+ c T→E ·
M ( v 1 )
·
(1
M ( v 2 ))]
c TT ·
k = j
k = i w ( v k )
LSP
+
(2)
δ = v i →...→v j ,
δ∈Δ π
 
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