On the complexity of adding convergence

Document Type

Conference Proceeding

Publication Date



Department of Computer Science


This paper investigates the complexity of designing Self-Stabilizing (SS) distributed programs, where an SS program meets two properties, namely closure and convergence. Convergence requires that, from any state, the computations of an SS program reach a set of legitimate states (a.k.a. invariant). Upon reaching a legitimate state, the computations of an SS program remain in the set of legitimate states as long as no faults occur; i.e., Closure. We illustrate that, in general, the problem of augmenting a distributed program with convergence, i.e., adding convergence, is NP-complete (in the size of its state space). An implication of our NP-completeness result is the hardness of adding nonmasking fault tolerance to distributed programs, which has been an open problem for the past decade.

Publication Title

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)