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Erschienen in:
2005 | OriginalPaper | Buchkapitel
Monte Carlo Model Checking
verfasst von : Radu Grosu, Scott A. Smolka
Erschienen in: Tools and Algorithms for the Construction and Analysis of Systems
Verlag: Springer Berlin Heidelberg
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We present
MC
2
, what we believe to be the first randomized, Monte Carlo algorithm for temporal-logic model checking. Given a specification
S
of a finite-state system, an LTL formula
ϕ
, and parameters
ε
and
δ
,
MC
2
takes
M
= ln (
δ
) / ln (1 –
ε
) random samples (random walks ending in a cycle, i.e
lassos
) from the Büchi automaton
B
=
B
S
×
B
¬
ϕ
. to decide if
L
(
B
) = ∅. Let
p
Z
be the expectation of an accepting lasso in
B
. Should a sample reveal an accepting lasso
l
,
MC
2
returns false with
l
as a witness. Otherwise, it returns true and reports that the probability of finding an accepting lasso through further sampling, under the assumption that
p
Z
≥
ε
, is less than
δ
. It does so in time
O
(
MD
) and space
O
(
D
), where
D
is
B
’s recurrence diameter, using an optimal number of samples
M
. Our experimental results demonstrate that
MC
2
is fast, memory-efficient, and scales extremely well.