Abstract
Zero-one exclusion is a family of distributed tasks indexed by n-bit Boolean signatures b[0], …b[n − 1]. We are interested in asynchronous computations where at most n + 1 asynchronous processes participate. They communicate with one another by reading and writing a shared memory, and halt after choosing a Boolean value. If m < n + 1 processes participate, then they must not all choose the value b[m − 1]. If all n + 1 processes participate, then they must not all choose the same value.
It is easy to show that some instances of zero-one exclusion are computationally difficult, in the sense that they cannot be solved by any algorithm in which asynchronous processes communicate by reading and writing a shared memory. Can we characterize the Boolean signatures for which zero-one exclusion does have an asynchronous read-write algorithm? We give a partial answer, which we feel is interesting because of the way it ties together distributed computability, combinatorial topology, and elementary number theory.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Attiya, H., Bar-Noy, A., Dolev, D., Peleg, D., Reischuk, R.: Renaming in an Asynchronous Environment. Journal of the ACM (July 1990)
Attiya, H., Castañeda, A., Herlihy, M., Paz, A.: Upper bound on the complexity of solving hard renaming. In: Proceedings of the 2013 ACM Symposium on Principles of Distributed Computing, PODC 2013, pp. 190–199. ACM, New York (2013)
Castañeda, A., Rajsbaum, S.: New combinatorial topology bounds for renaming: the lower bound. Distributed Computing 22, 287–301 (2010), 10.1007/s00446-010-0108-2
Chaudhuri, S.: Agreement Is Harder Than Consensus: Set Consensus Problems in totally asynchronous systems. In: Proceedings of The Ninth Annual ACM Symosium on Principles of Distributed Computing, pp. 311–234 (August 1990)
Gafni, E.: The 0—1-exclusion families of tasks. In: Baker, T.P., Bui, A., Tixeuil, S. (eds.) OPODIS 2008. LNCS, vol. 5401, pp. 246–258. Springer, Heidelberg (2008)
Gafni, E., Rajsbaum, S., Herlihy, M.P.: Subconsensus Tasks: Renaming Is Weaker Than Set Agreement. In: Dolev, S. (ed.) DISC 2006. LNCS, vol. 4167, pp. 329–338. Springer, Heidelberg (2006)
Herlihy, M.: Wait-free synchronization. ACM Trans. Program. Lang. Syst. 13(1), 124–149 (1991)
Herlihy, M., Kozlov, D., Rajsbaum, S.: Distributed Computing Through Combinatorial Topology. Elsevier Science (2013)
Herlihy, M., Shavit, N.: The topological structure of asynchronous computability. J. ACM 46(6), 858–923 (1999)
Kozlov, D.N.: Weak symmetry breaking and abstract simplex paths (2013) (preprint)
Munkres, J.: Elements of Algebraic Topology, 2nd edn. Prentice Hall (January 1984)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gafni, E., Herlihy, M. (2014). Sporadic Solutions to Zero-One Exclusion Tasks. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43948-7_1
Download citation
DOI: https://doi.org/10.1007/978-3-662-43948-7_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-43947-0
Online ISBN: 978-3-662-43948-7
eBook Packages: Computer ScienceComputer Science (R0)