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10
Concurrent Systems/notes/10 - Consensus Implementation.md
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@ -13,7 +13,15 @@ For all T, CN(T) > 0; if there is no sup, we let CN(T) := +∞
- contradiction with CN(T1) < n - contradiction with CN(T1) < n
### Schedules and Configurations ### Schedules and Configurations
**Schedule:** sequence of operation invocations issued by processes **Schedule:** sequence of operation invocations issued by processes.
**Configuration:** the global state of a system at a given execution time (values of the shared memory + local state of every process). **Configuration:** the global state of a system at a given execution time (values of the shared memory + local state of every process).
Given a configuration C and a schedule S, we denote with S(C) the configuration obtained starting from C and applying S. Given a configuration C and a schedule S, we denote with S(C) the configuration obtained starting from C and applying S.
Let's consider binary consensus implemented by an algorithm A by using base objects and atomic R/W registers; let us call $S_A$ a schedule induced by A.
A configuration C obtained during the execution of all A is called:
- **v-valent** if $S_A(C)$ decides v, for every $S_A$
- **monovalent**, if there exists $v \in \{0,1\}$ s.t. C is v-valent
- **bivalent**, otherwise.