10,523 research outputs found
A linear time algorithm for the orbit problem over cyclic groups
The orbit problem is at the heart of symmetry reduction methods for model
checking concurrent systems. It asks whether two given configurations in a
concurrent system (represented as finite strings over some finite alphabet) are
in the same orbit with respect to a given finite permutation group (represented
by their generators) acting on this set of configurations by permuting indices.
It is known that the problem is in general as hard as the graph isomorphism
problem, whose precise complexity (whether it is solvable in polynomial-time)
is a long-standing open problem. In this paper, we consider the restriction of
the orbit problem when the permutation group is cyclic (i.e. generated by a
single permutation), an important restriction of the problem. It is known that
this subproblem is solvable in polynomial-time. Our main result is a
linear-time algorithm for this subproblem.Comment: Accepted in Acta Informatica in Nov 201
Liveness of Randomised Parameterised Systems under Arbitrary Schedulers (Technical Report)
We consider the problem of verifying liveness for systems with a finite, but
unbounded, number of processes, commonly known as parameterised systems.
Typical examples of such systems include distributed protocols (e.g. for the
dining philosopher problem). Unlike the case of verifying safety, proving
liveness is still considered extremely challenging, especially in the presence
of randomness in the system. In this paper we consider liveness under arbitrary
(including unfair) schedulers, which is often considered a desirable property
in the literature of self-stabilising systems. We introduce an automatic method
of proving liveness for randomised parameterised systems under arbitrary
schedulers. Viewing liveness as a two-player reachability game (between
Scheduler and Process), our method is a CEGAR approach that synthesises a
progress relation for Process that can be symbolically represented as a
finite-state automaton. The method is incremental and exploits both
Angluin-style L*-learning and SAT-solvers. Our experiments show that our
algorithm is able to prove liveness automatically for well-known randomised
distributed protocols, including Lehmann-Rabin Randomised Dining Philosopher
Protocol and randomised self-stabilising protocols (such as the Israeli-Jalfon
Protocol). To the best of our knowledge, this is the first fully-automatic
method that can prove liveness for randomised protocols.Comment: Full version of CAV'16 pape
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