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) [AbJo:lossy:IC] 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 [BaEn:plcs,ABIJ:problossy] 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 [BaEn:plcs,ABIJ:problossy]. More precisely, we assume that during each step in the execution of the system, each message may be lost with a certain predefined probability. We show that for such systems the following model checking problem is decidable: to verify whether a given property definable by finite state omega-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.
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