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## Commutativity Specifications  Though *commutativity* is often discussed in terms of an operation commuting with all other operations, it is actually more nuanced. If a pair of operations commute, then executing them in either order will produce the same result. Using the definitions from \cite{Kulkarni:PLDI11}, whether or not a pair of method invocations commute is a property of the data type and is a function of the methods, their arguments, their return values, and the *abstract* state of their target. We call the full set of commutativity rules for a data type its *commutativity specification.* An example specification for a *set* is shown in Table \cite{spec}. \cite{tab:spec}.  ## Transaction Boosting  If two operations in different transactions commute with each other, it means they could execute in any order,