A rigorous analysis of concurrent operations on B-trees

Abstract

An account is given of a rigorous study of concurrent operations on a variant of the B-tree in the framework of a general theory of concurrent systems, an extension of the r-calculus. The assertion of correctness of the algorithms is that the agent representing the system is behaviourally equivalent to an agent whose observable behaviour describes simply the expected interactions of the system with its environment. An outline of the proofs of correctness of algorithms for insertion and search is given. Algorithms for deletion and compression are considered briefly. The main theoretical contribution is an extension of the theory of partial confluence of agents. © Springer-Verlag Berlin Heidelberg 1997.