Skip to main content
Log in

Connectivity requirements for Byzantine agreement under restricted types of failures

  • Published:
Distributed Computing Aims and scope Submit manuscript


We investigate the problem of reaching Byzantine Agreement in arbitrary networks where both processors and communication links are subject to omission or stopping faults. For the case of deterministic, synchronous algorithms we give a necessary and sufficient condition relating the solvability of the problem to the connectivity of the network. In particular, we show that an algorithm resilient to at mostt faulty processors andk faulty links subject to omission or stopping faults exist, if and only if the network has a connectivity pair (t′, k′)>(t, k).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  • Dolev D (1982) The Byzantine generals strike again. J Algorithms 3(1):14–30

    Google Scholar 

  • Dolev D, Dwork C, Stockmeyer L (1983) On the minimum synchronism needed for distributed consensus. Proc 24th Annual Symp on Foundations of Comput Sci, IEEE Computer Society, Tucson, AZ (November 1983)

  • Dolev D, Strong HR (1982) Distributed commit with bounded waiting. Proc 2nd IEEE Symp on Reliability in Dist'd Software and Database Systems, Pittsburgh, PA, pp 53–60

  • Dolev D, Strong HR (1983) Authenticated algorithms for Byzantine Agreement. SIAM J Comput 12(4):656–666

    Google Scholar 

  • Dolev D, Fischer MJ, Fowler RJ, Lynch NA, Strong HR (1982) An efficient algorithm for Byzantine Agreement without authentication. Inf Control 52(3):256–274

    Google Scholar 

  • Fischer MJ (1983) The consensus problem in unreliable distributed systems (a brief survey). Tech Rep 273, Dept Comput Sci, Yale University (June 1983)

  • Fischer MJ, Lynch NA, Merritt M (1986) Easy impossibility proofs for distributed consensus problems. Proc 4th ACM Symp on Principles of Distributed Computing, Minaki, Ontario, Canada (August 1986), pp 59–70

  • Gray JN (1978) Notes on database operating systems. In: Bayer R, Graham RM, Seegmuller G (eds) Operating systems: An advanced course. Lect Notes Comput Sci, vol. 60 Springer, Berlin Heidelberg New York

    Google Scholar 

  • Hadzilacos V (1984) Issues of fault tolerance in concurrent computations. PhD dissertation, Harvard University

  • Hadzilacos V (1986) On the relationship between the atomic commitment and consensus problems. Workshop on Fault Tolerant Distributed Computing, Pacific Grove, CA, USA (April 1986)

  • Lamport L, Shostak R, Pease M (1982) The Byzantine generals problem. ACM Trans Programm Lang Syst 4(3):382–401

    Google Scholar 

  • Lamport L (1983) The weak Byzantine generals problem. J ACM 30(3):668–676

    Google Scholar 

  • Menger K (1927) Zur allgemeinen Kurventheorie. Fundam Math 10:96–115

    Google Scholar 

  • Pease M, Shostak R, Lamport L (1980) Reaching agreement in the presence of faults. J ACM 27(2):228–234

    Google Scholar 

  • Reischuk R (1982) A new solution for the Byzantine generals problem. IBM Res Rep RJ 3673 (November 1982)

  • Skeen MD (1982) Crash recovery in a distributed database system. PhD dissertation, Dept EECS, University of California at Berkeley

Download references

Author information

Authors and Affiliations


Additional information

Vassos Hadzilacos received his BSE from Princeton in 1980 and his PhD from Harvard in 1984, both in Computer Science. He is presently an Assistant Professor at University of Toronto. His research interests are synchronisation and reliability in distributed computing. He is a co-author of a book on Concurrency Control and Reliability in Database Systems.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hadzilacos, V. Connectivity requirements for Byzantine agreement under restricted types of failures. Distrib Comput 2, 95–103 (1987).

Download citation

  • Issue Date:

  • DOI: