Pseudo-stabilizing causal ordering

Causal ordering finds its usage in many distributed appications like replicated data management, distributed systems monitoring, synchronizing multimedia streams and other applications frequently involving human interactions. The concept of self-stabilization has gathered significant recognition in distributed systems. Many self-stabilizing algorithms have been proposed for various problems in a distributed system. A self-stabilizing distributed system ensures recovery from an illegitimate state to a legitimate state in a finite number of steps. Pseudo-stabilization is a weaker form of self-stabilization which ensures that a system when started in arbitrary state is guaranteed to eventually recover to a legitimate state. In this paper we propose a pseudo-stabilizing algorithm for causal order delivery of messages in a distributed system and prove its correctness.