# On the Use of Model Checking for the Bounded and Unbounded Verification of Nonblocking Concurrent Data Structures

Concurrent data structure algorithms have traditionally been designed using locks to regulate the behaviour of interacting threads, thus restricting access to parts of the shared memory to only one thread at a time. Since locks can lead to issues of performance and scalability, there has been interest in designing so-called nonblocking algorithms that do not use locks. However, designing and reasoning about concurrent systems is difficult, and is even more so for nonblocking systems, as evidenced by the number of incorrect algorithms in the literature. This thesis explores how the technique of model checking can aid the testing and verification of nonblocking data structure algorithms. Model checking is an automated verification method for finite state systems, and is able to produce counterexamples when verification fails. For verification, concurrent data structures are considered to be infinite state systems, as there is no bound on the number of interacting threads, the number of elements in the data structure, nor the number of possible distinct data values. Thus, in order to analyse concurrent data structures with model checking, we must either place finite bounds upon them, or employ an abstraction technique that will construct a finite system with the same properties. First, we discuss how nonblocking data structures can be best represented for model checking, and how to specify the properties we are interested in verifying. These properties are the safety property linearisability, and the progress properties wait-freedom, lock-freedom and obstructionfreedom. Second, we investigate using model checking for exhaustive testing, by verifying bounded (and hence finite state) instances of nonblocking data structures, parameterised by the number of threads, the number of distinct data values, and the size of storage memory (e.g. array length, or maximum number of linked list nodes). It is widely held, based on anecdotal evidence, that most bugs occur in small instances. We investigate the smallest bounds needed to falsify a number of incorrect algorithms, which supports this hypothesis. We also investigate verifying a number of correct algorithms for a range of bounds. If an algorithm can be verified for bounds significantly higher than the minimum bounds needed for falsification, then we argue it provides a high degree of confidence in the general correctness of the algorithm. However, with the available hardware we were not able to verify any of the algorithms to high enough bounds to claim such confidence. Third, we investigate using model checking to verify nonblocking data structures by employing the technique of canonical abstraction to construct finite state representations of the unbounded algorithms. Canonical abstraction represents abstract states as 3-valued logical structures, and allows the initial coarse abstraction to be refined as necessary by adding derived predicates. We introduce several novel derived predicates and show how these allow linearisability to be verified for linked list based nonblocking stack and queue algorithms. This is achieved within the standard canonical abstraction framework, in contrast to recent approaches that have added extra abstraction techniques on top to achieve the same goal. The finite state systems we construct using canonical abstraction are still relatively large, being exponential in the number of distinct abstract thread objects. We present an alternative application of canonical abstraction, which more coarsely collapses all threads in a state to be represented by a single abstract thread object. In addition, we define further novel derived predicates, and show that these allow linearisability to be verified for the same stack and queue algorithms far more efficiently.