Global state collection

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Global state collection

• Chandy Lamport algorithm does a partial job.
  Each process collects a fragment of the global
  state, but these pieces have to be put together.
• Applications
• - computing network topology
• - termination detection
• - deadlock detection
• etc

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A simple exercise

• Collect global state
• via all-to-all broadcast
• At the end, each process
• will compute a set V, where
• V s(i) 0 i N-1

s(i)
s(j)
i
j
s(k)
s(l)
k
l
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A simple exercise

• Program broadcast (for process i
• define V.i, W.i set of values
• initially V.is(i), W.i ??
• ?and?every channel is empty?
• do V.i ? W.i? send (V.i \ W.i) to every outgoing
  channel W.i V.i
• ? empty (k, i)? receive X from channel (k, i)
  V.i V.i ? X
• od

V.i W.i
V.k W.k
(i,k)
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Proof

• empty (i. k) ? W.i ?? V.k.
• (Upon termination) ?i V.i W.i,
• and all channels are empty.
• So, V.i ?? V.k.
• On a cyclic path, V.i V.k must be
• true. Since s(i) ??V.i, s(i) ??V.k

V.i W.i
V.k W.k
(i,k)
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Termination detection

• In a network, processes may be active or passive.
• Termination implies
• (a) every process is passive,
• (b) all channels are empty, and
• (c) the global state of the system satisfies
  the
• desired postcondition

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Termination detection
The progress of a computation. Notice how one
process engages another process. Eventually All
processes turn white - this signals termination.
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Dijkstra-Scholten algorithm

• An initiator initiates termination
• detection by sending a signal
• down the edge when it engages
• another node.
• At a suitable time, the recipient
• sends an ack back.
• When the initiator receives ack, it
• detects termination.

• Node j engages node k.

j
k
j
k
j
k
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Dijkstra-Scholten algorithm

• Deficit (e) of signals on e - of ack on e
• For any node,
• C deficit along incoming edges
• D deficit along outgoing edges edges
• Invariant 1. (C 0) ? (D 0)
• Invariant 2. (C gt 0) ? (D 0)

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Dijkstra-Scholten algorithm

• Invariant 1. (C 0) ? (D 0)
• Invariant 2. (C gt 0) ? (D 0)
• The invariants must hold when
• an interim node sends an ack.
• So
• (C-1 0) ? (C-1gt 0 ??D0)
• follows from INV1 and INV2
• (Cgt1) ?? (C1 ? D0)
• (Cgt1) ??(C1 ? D0)

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Dijkstra-Scholten algorithm

• program detect for an internal node i
• initially C0, D0, parent i
• do m signal ? (C0) ?
• C1 state active parent sender
• m ack ? D D-1
• (C1? D0) ? state passive ?
• send ack to parent C 0 parent i
• m signal ? (C1) ?
• send ack to the sender
• od

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Dijkstra-Scholten algorithm

• The engagement edges form a spanning tree. The
  tree grows and shrinks.
• Signals are acknowledged on very-first-in-very-las
  t-out basis
• Termination is detected when the initiator
  receives ack.

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