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Abstract:

• Recap: observation in (fault-free) asynchronous systems (7 slides). • Recap: modalities possibly and definitely (2 slides). • Observation in asynchronous systems with crash faults (5 slides). • Modalities negotiably and discernibly (4 slides). • Base idea of detection algorithms (6 slides). 3/30 Asynchronous systems • Set of n application processes p1,..., pn connected by a communication network. • Communication by message passing using send and receive commands. • Messages can take arbitrarily long. • Processes can be arbitrarily slow. • Very weak assumptions → very realistic model. top 4/30 Observation in asynchronous systems • Distributed computation in which events occur. • For every relevant event, a control message is broadcast to a set of monitor processes. p1 p2 5/30 Observation in asynchronous systems • Distributed computation in which events occur. • For every relevant event, a control message is broadcast to a set of monitor processes. m1 p1 p2 m2 • Global state = “cut ” through the diagram. • Monitors construct a sequence of global states Σ = S1, S2,... • Σ is called an observation. 5/30 • Given predicate ϕ on global states. • Devise an algorithm with: Predicate detection – (safety) no false detections of ϕ. – (liveness) if ϕ holds, it is eventually detected. • Naive approach: monitors check every Si for ϕ. 6/30 • Detection predicate is ϕ ≡ x = y • “ϕ holds? ” is not observer-invariant! m1 p1 p2 m2 Difficulties of observation x = 0 y = 1 x: = 1 y: = 2 ϕ holds!!! 7/30 Lattice of all global states • Look at set of all (possibly) global states. • Take relation on how one set evolves from another by executing a single event. ⇒ Lattice of global states. • Observation is a path through the lattice. 8/30 p1 p2 Lattice example e 1 1 e 1 2 e 1 3 e 2 1 e 2 2 e 2 3 p1 p2

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