On the Complexity of Adding Convergence

• Published in: Fundamentals of Software Engineering Vol. 8161; pp. 17 - 33
• Main Authors: Klinkhamer, Alex, Ebnenasir, Ali
• Format: Book Chapter
• Language: English
• Published: Germany Springer Berlin / Heidelberg 2013; Springer Berlin Heidelberg
• Series: Lecture Notes in Computer Science
• Subjects: Convergence; NP-Completeness; Self-Stabilization
• ISBN: 3642402127; 9783642402128
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-642-40213-5_2

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.