  Linearizability is a well-established consistency and correctness criterion
for concurrent data types. An important feature of linearizability is Herlihy
and Wing's locality principle, which says that a concurrent system is
linearizable if and only if all of its constituent parts (so-called objects)
are linearizable. This paper presents $P$-compositionality, which generalizes
the idea behind the locality principle to operations on the same concurrent
data type. We implement $P$-compositionality in a novel linearizability
checker. Our experiments with over nine implementations of concurrent sets,
including Intel's TBB library, show that our linearizability checker is one
order of magnitude faster and/or more space efficient than the state-of-the-art
algorithm.
