Verification of Probabilistic Systems with Faulty Communication
Many protocols are designed to operate correctly even in the case where the underlying communication medium is faulty. To capture the behaviour of such protocols,lossy channel systems (LCS) [AJ96b ] have been proposed.In an LCS the communication channels are modelled as FIFO buffers which are unbounded,but also unreliable in the sense that they can nondeterministically lose messages.
Recently,several attempts [BE99,ABIJ00 ]have been made to study probabilistic Lossy Channel Systems (PLCS) in which the probability of losing messages is taken into account.In this paper,we consider a variant of PLCS which is more realistic than those studied in [BE99,ABIJ00 ]. More precisely,we assume that during each step in the execution of the system,each message may be lost with a certain prede fined probability. We show that for such systems the following model checking problem is decidable: to verify whether a given property de finable by finite state ω -automata holds with probability one.We also consider other types of faulty behavior,such as corruption and duplication of messages,and insertion of new messages,and show that the decidability results extend to these models.
- [ABIJ00]Parosh Aziz Abdulla, Christel Baier, Purushothaman Iyer,and Bengt Jonsson.Reasoning about probabilistic lossy channel systems.In C. Palamidessi, editor,Proc. CONCUR 2000, 11th Int. Conf. on Concurrency Theory volume 1877 of Lecture Notes in Computer Science 2000.Google Scholar
- [BE99]C. Baier and B. Engelen.Establishing qualitative properties for probabilistic lossy channel systems.In Katoen,editor,ARTS’99, Formal Methods for Real-Time and Probabilistic Systems, 5th Int. AMAST Workshop volume 1601 of Lecture Notes in Computer Science pages 34–52.Springer Verlag, 1999.Google Scholar
- [Boc78]G.V. Bochman.Finite state description of communicating protocols.Computer Networks 2:361–371,1978.Google Scholar
- [BS03]N. Bertrand and Ph. Schnoebelen.Model checking lossy channels systems is probably decidable.In Proc. FOSSACS03, Conf. on Foundations of Software Science and Computation Structures 2003.Google Scholar
- [Hig52]G. Higman.Ordering by divisibility in abstract algebras.Proc. London Math. Soc.2:326–336,1952.Google Scholar
- [KSK66]J.G. Kemeny, J.L. Snell,and A.W. Knapp.Denumerable Markov Chains D Van Nostad Co.,1966.Google Scholar
- [Tho90]W. Thomas.Automata on infinite objects.In Handbook of Theoretical Computer Science, Volume B: Formal Methods and Semantics pages 133–192,1990.Google Scholar