Formal Verification through Combinatorial Topology: the CAS-Extended Model

Abstract

Wait-freedom guarantees that all processes complete their operations in a finite number of steps regardless of the delay of any process. Combinatorial topology has been proposed in the literature as a formal verification technique to prove the wait-free computability of decision tasks. Wait-freedom is proved through the properties of a static topological structure that expresses all possible combinations of execution paths of the protocol solving the decision task. The practical application of combinatorial topology as a formal verification technique is limited because the existing theory only considers protocols in which the manner of communication between processes is through read-write memory. This research proposes an extension to the existing theory, called the CAS-extended model. The extended theory includes Compare-And-Swap (CAS) and Load-Linked/Store-Conditional (LL/SC) which are atomic primitives used to achieve wait-freedom in state-of-the-art protocols. The CAS-extended model theory can be used to formally verify wait-free algorithms used in practice, such as concurrent data structures. We present new definitions detailing the construction of a protocol complex in the CAS-extended model. As a proof-of-concept, we formally verify a wait-free queue with three processes using the CAS-extended combinatorial topology.