Decision Procedures for the Temporal Verification of Concurrent Data Structures

Concurrent datatypes are concurrent implementation of classical data abstractions, specifically designed to exploit the great deal of parallelism available in multiprocessor and multicore architectures. The correctness of concurrent datatypes is essential for the overall correctness of the system. In this work we study the problem of aiding in the automation of temporal verification of concurrent datatypes. The main difficulty to reason about these datatypes comes from the combination of their inherently high concurrency and the manipulation of dynamic memory. Most previous approaches to verification of concurrent datatypes try to enrich separation logic to deal with concurrency, leveraging on the success of separation logic in reasoning about sequential heap algorithms. This work contains two contributions. First, we present a complementary approach to the verification of concurrent data structures: we start from deductive temporal verification, a very powerful technique to reason about concurrent systems, and enrich it to cope with dynamic memory. The verification process uses verification diagrams and explicit region annotations. In the end, each proof is decomposed into a sequence of verification conditions. The literals involved in these verification conditions depend mainly on the data structured being verified. The second, and main, contribution consists in two decision procedures for specific data-types: concurrent lock-coupling singly-linked lists and concurrent skiplists. These decision procedures are capable of reasoning about regions, pointers, lisp-like lists and ordered lists allowing automatic verification of generated verification conditions. We show how using our technique we are able to prove not only safety but also liveness properties of a version of concurrent lists and express the preservation of skiplist shape by a data structure. Moreover, the approach we present can be easily extended for using it in the verification of a wide range of similar concurrent datatypes including hash maps and graphs.