TY - GEN
T1 - Counting-based impossibility proofs for renaming and set agreement
AU - Attiya, Hagit
AU - Paz, Ami
N1 - Funding Information: This research is supported in part by Yad-HaNadiv fund and the Israel Science Foundation (grant number 1227/10).
PY - 2012
Y1 - 2012
N2 - Renaming and set agreement are two fundamental sub-consensus tasks. In the M-renaming task, processes start with names from a large domain and must decide on distinct names in a range of size M; in the k-set agreement task, processes must decide on at most k of their input values. Renaming and set agreement are representatives of the classes of colored and colorless tasks, respectively. This paper presents simple proofs for key impossibility results for wait-free computation using only read and write operations: n processes cannot solve (n - 1)-set agreement, and, if n is a prime power, n processes cannot solve (2n - 2)-renaming. Our proofs consider a restricted set of executions, and combine simple operational properties of these executions with elementary counting arguments, to show the existence of an execution violating the task's requirements. This makes the proofs easier to understand, verify, and hopefully, extend.
AB - Renaming and set agreement are two fundamental sub-consensus tasks. In the M-renaming task, processes start with names from a large domain and must decide on distinct names in a range of size M; in the k-set agreement task, processes must decide on at most k of their input values. Renaming and set agreement are representatives of the classes of colored and colorless tasks, respectively. This paper presents simple proofs for key impossibility results for wait-free computation using only read and write operations: n processes cannot solve (n - 1)-set agreement, and, if n is a prime power, n processes cannot solve (2n - 2)-renaming. Our proofs consider a restricted set of executions, and combine simple operational properties of these executions with elementary counting arguments, to show the existence of an execution violating the task's requirements. This makes the proofs easier to understand, verify, and hopefully, extend.
UR - http://www.scopus.com/inward/record.url?scp=84868356406&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-33651-5_25
DO - 10.1007/978-3-642-33651-5_25
M3 - منشور من مؤتمر
SN - 9783642336508
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 356
EP - 370
BT - Distributed Computing - 26th International Symposium, DISC 2012, Proceedings
T2 - 26th International Symposium on Distributed Computing, DISC 2012
Y2 - 16 October 2012 through 18 October 2012
ER -