IST Austria Technical Report

Linearizability requires that the outcome of calls by competing threads to a concurrent data structure is the same as some sequential execution where each thread has exclusive access to the data structure. In an ordered data structure, such as a queue or a stack, linearizability is ensured by requiring threads commit in the order dictated by the sequential semantics of the data structure; e.g., in a concurrent queue implementation a dequeue can only remove the oldest element. In this paper, we investigate the impact of this strict ordering, by comparing what linearizability allows to what existing implementations do. We first give an operational definition for linearizability which allows us to build the most general linearizable implementation as a transition system for any given sequential specification. We then use this operational definition to categorize linearizable implementations based on whether they are bound or free. In a bound implementation, whenever all threads observe the same logical state, the updates to the logical state and the temporal order of commits coincide. All existing queue implementations we know of are bound. We then proceed to present, to the best of our knowledge, the first ever free queue implementation. Our experiments show that free implementations have the potential for better performance by suffering less from contention

Formal verification of a concurrent binary search tree

In this thesis, we formally verify a simplified version of the non-blocking linearizable binary search tree of Ellen et al., which appeared in the Proceedings of the 29th Annual ACM Symposium on Principles of Distributed Computing (pages 131-140), using the PVS specification and verification system. The algorithm and its specification are both modelled as I/O automata. In order to formally verify that the algorithm implements the specification, we show that the algorithm's I/O automaton simulates the specification's. An intermediate I/O automaton is constructed to simplify the simulation proof of linearizability. By showing there is a forward simulation from the algorithm's I/O automaton to the intermediate automaton and there is a backward simulation from the intermediate automaton to the specification's automaton, we formally verify that the algorithm implements its specification. While formalizing the proof, we found small errors in the original proof