Affiliation:
1. Michigan State University, U.S.A.
2. Université de Paris and CNRS, France
3. Universidad Nacional Autónomade México, México
4. University of Bordeaux and CNRS, France
Abstract
Runtime verification
is a lightweight method for monitoring the formal specification of a system during its execution. It has recently been shown that a given state predicate can be monitored consistently by a set of crash-prone asynchronous
distributed
monitors observing the system, only if each monitor can emit verdicts taken from a
large enough
finite set. We revisit this impossibility result in the concrete context of linear-time logic (
ltl
) semantics for runtime verification, that is, when the correctness of the system is specified by an
ltl
formula on its execution traces. First, we show that monitors synthesized based on the 4-valued semantics of
ltl
(
rv-ltl
) may result in inconsistent distributed monitoring, even for some simple
ltl
formulas. More generally, given any
ltl
formula φ, we relate the number of different verdicts required by the monitors for consistently monitoring φ, with a specific structural characteristic of φ called its
alternation number
. Specifically, we show that, for every
k ≥ 0
, there is an
ltl
formula φ with alternation number
k
that cannot be verified at runtime by distributed monitors emitting verdicts from a set of cardinality smaller than
k
+ 1. On the positive side, we define a family of logics, called
distributed
ltl
(abbreviated as
dltl
), parameterized by
k
≥ 0, which refines
rv-ltl
by incorporating
2k
+ 4 truth values. Our main contribution is to show that, for every
k
≥ 0, every
ltl
formula φ with alternation number
k
can be consistently monitored by distributed monitors, each running an automaton based on a (2 ⌈
k
/2 ⌉ +4)-valued logic taken from the
dltl
family.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
2 articles.
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