Proving Linearizability Using Forward Simulations

Linearizability is the standard correctness criterion concurrent datastructures such as stacks and queues. It allows to establish observational refine-ment between a concurrent implementation and an atomic reference implemen-tation. Proving linearizability requires identifying linearization points for eachmethod invocation along all possible computations, leading to valid sequentialexecutions, or alternatively, establishing forward and backward simulations. Inboth cases, carrying out proofs is hard and complex in general. In particular,backward reasoning is difficult in the context of programs with data structures,and strategies for identifying statically linearization points cannot be defined forall existing implementations. In this paper, we show that, contrary to commonbelief, many such complex implementations, including, e.g., the Herlihy&Wing;Queue and the Time-Stamped Stack, can be proved correct using only forwardsimulation arguments. This leads to simple and natural correctness proofs forthese implementations that are amenable to automation.