Property assessment of Peterson's mutual exclusion algorithms

Abstract

<p>The goal of this work was to experiment with the formal modeling and automated reasoning of concurrent/parallel systems, mainly focusing on mutual exclusion algorithms. A concrete method is presented, which depends on timed automata and the model checker provided by the popular Uppaal toolbox. The method can be used for a thorough assessment of the properties of mutual exclusion algorithms. The paper argues that the proposed approach can be effective in moving beyond informal and intuitive reasoning about concurrency, which can be challenging due to the non-determinism and interleaving of the action execution order of the involved processes. The approach is described and applied to an in-depth analysis of Peterson's algorithms for $ N = 2 $ and $ N &gt; 2 $ processes. The analysis allows the reconciliation of different evaluations reported in the literature, particularly for the overtaking bound, and also reveals new results not previously disclosed. The general case of $ N &gt; 2 $ was handled within the context of the state-of-art, standard, and efficient tournament binary-tree organization, which uses the solution for two processes to arbitrate between pairs of processes at different stages of their upward movement along the tree. All mutual exclusion algorithms are investigated under both atomic and non-atomic memory models.</p>