A Lightweight Method for Automated Design of Convergence in Network Protocols

Abstract

Design and verification of Self-Stabilizing (SS) network protocols are difficult tasks in part because of the convergence property that requires an SS protocol to recover to a set of legitimate states from any state in its state space. Once an SS protocol reaches a legitimate state, it remains in the set of legitimate states as long as there are no faults, called the closure property. Distribution issues exacerbate the design complexity of SS protocols as processes should collaborate and take local actions that result in global convergence. Most existing design techniques are manual, and mainly focus on protocols whose global state can be corrected if the local states of all processes are corrected, called the locally correctable protocols. After manual design, an SS protocol has to be verified for closure and convergence. Previous work observes that verifying SS protocols is a harder problem than designing them as developers have to ensure the correctness of closure and convergence functionalities and their noninterference. An algorithmic method for the design of convergence generates protocols that are correct by construction, thereby eliminating the need for verification.

In order to facilitate the design of SS protocols, this article presents a lightweight method for algorithmic addition of convergence to finite-state nonstabilizing protocols, including nonlocally correctable protocols. The proposed method enables the reuse of design efforts in the development of different self-stabilizing protocols. Moreover, for the first time (to the best of our knowledge), this article presents an algorithmic method for the addition of convergence to symmetric protocols that consist of structurally similar processes. The proposed approach is supported by a software tool that automatically adds convergence to nonstabilizing protocols. We have used the proposed method/tool to automatically generate several self-stabilizing protocols with up to 40 processes (and 3⁴⁰ states) in a few minutes on a regular PC. Surprisingly, our tool has synthesized both protocols that are the same as their manually designed versions as well as alternative solutions for well-known problems in the literature (e.g., Dijkstra’s token ring, maximal matching, graph coloring, agreement and leader election in a ring). Moreover, the proposed method has helped us detect a design flaw in a manually designed self-stabilizing protocol.

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Index Terms

• Applied computing

  • Arts and humanities

    • Architecture (buildings)

      • Computer-aided design

  • Physical sciences and engineering

    • Engineering

      • Computer-aided design

• General and reference

  • Cross-computing tools and techniques

    • Reliability

• Mathematics of computing

  • Mathematical software

• Networks

  • Network protocols

    • Protocol correctness

      • Protocol testing and verification

• Software and its engineering

  • Software creation and management

    • Software verification and validation

      • Formal software verification

  • Software organization and properties

    • Extra-functional properties

      • Software fault tolerance

      • Software reliability

    • Software functional properties

      • Formal methods

• Theory of computation

  • Logic

  • Semantics and reasoning

    • Program reasoning