The Verified Incremental Design of a Distributed Spanning Tree Algorithm: Extended Abstract

Abstract. The paper announces an incremental mechanically–verified design of the algorithm of Gallager, Humblet, and Spira for the distributed determination of the minimum-weight spanning tree in a graph of processes. The processes communicate by means of asynchronous messages with their neighbours in the graph. Messages over one link may pass each other. The proof of the algorithm is based on ghost variables, invariants, and a decreasing variant function. The verification is mechanized by means of the theorem prover Nqthm of Boyer and Moore. This extended abstract is an introduction to the full paper that can be obtained by ftp (http://link.springer.de/link/service/journals/00165/).

[1]  Seif Haridi,et al.  Distributed Algorithms , 1992, Lecture Notes in Computer Science.

[2]  Nancy A. Lynch,et al.  Distributed Algorithms , 1992, Lecture Notes in Computer Science.

[3]  Pierre A. Humblet,et al.  A Distributed Algorithm for Minimum-Weight Spanning Trees , 1983, TOPL.

[4]  Job Zwiers,et al.  Partial Order Based Design of Concurrent Systems , 1993, REX School/Symposium.

[5]  Hesselink.  Incremental Design of a Distributed Spanning Tree Algorithm , 2022 .

[6]  Wim H. Hesselink,et al.  A mechanical proof of Segall's PIF algorithm , 1997, Formal Aspects of Computing.

[7]  Robert S. Boyer,et al.  A computational logic handbook , 1979, Perspectives in computing.

[8]  N. Lynch,et al.  A Lattice-Structured Proof Technique Applied to a Minimum Spanning Tree Algorithm , 1988 .

[9]  Robert E. Tarjan,et al.  Data structures and network algorithms , 1983, CBMS-NSF regional conference series in applied mathematics.

[10]  Nancy A. Lynch,et al.  A lattice-structured proof of a minimum spanning , 1988, PODC '88.

[11]  Eli Gafni,et al.  Understanding and verifying distributed algorithms using stratified decomposition , 1988, PODC '88.