Consider the following classes of schedules: serializable and 2PL. For each of t
ID: 3790801 • Letter: C
Question
Consider the following classes of schedules: serializable and 2PL. For each of the following schedules, state which of the preceding classes it belongs to. If you cannot decide whether a schedule belongs in a certain class based on the listed actions, explain briefly. The actions are listed in the order they are scheduled and prefixed with the transaction name. If a commit or abort is not shown, the schedule is incomplete; assume that abort or commit must follow all the listed actions. T1:R(X), T2:R(Y), T3:W(X), T2:R(X), T1:R(Y) T1:R(X), T1:R(Y), T1:W(X), T2:R(Y), T3:W(Y), T1:W(X), T2:R(Y) T1:W(X), T2:R(X), T1:W(X), T2:Commit, T1:Commit T1:R(X), T2:W(X), T1:W(X), T3:R(X), T1:Commit, T2:Commit, T3:CommitExplanation / Answer
This integer is allowed to be different for each pair of states, hence the subscripts in nij. Allowing n to be zero means that every state is accessible from itself by definition. The accessibility relation is reflexive and transitive, but not necessarily symmetric.
A state i is said to communicate with state j (written i j) if both i j and j i. A communicating class a maximal set of states C such that every pair of states in C communicates with each other. Communication is an equivalence relation, and communicating classes are the equivalence classes of this relation.
A communicating class is closed if the probability of leaving the class is zero, namely if i is in C but j is not, then j is not accessible from i. The set of communicating classes forms a directed, acyclic graph by inheriting the arrows from the original state space. A communicating class is closed if and only if it has no outgoing arrows in this graph.
A state i is said to be essential or final if for all j such that i j it is also true that j i. A state i is inessential if it is not essential.[40] A state is final if and only if its communicating class is closed.
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