TY - GEN
T1 - Not all fair probabilistic schedulers are equivalent
AU - Chatzigiannakis, Ioannis
AU - Dolev, Shlomi
AU - Fekete, Sándor P.
AU - Michail, Othon
AU - Spirakis, Paul G.
PY - 2009/12/31
Y1 - 2009/12/31
N2 - We propose a novel, generic definition of probabilistic schedulers for population protocols. We then identify the consistent probabilistic schedulers, and prove that any consistent scheduler that assigns a non-zero probability to any transition i → j, where i and j are configurations satisfying i ≠ j, is fair with probability 1. This is a new theoretical framework that aims to simplify proving specific probabilistic schedulers fair. In this paper we propose two new schedulers, the State Scheduler and the Transition Function Scheduler. Both possess the significant capability of being protocol-aware, i.e. they can assign transition probabilities based on information concerning the underlying protocol. By using our framework we prove that the proposed schedulers, and also the Random Scheduler that was defined by Angluin et al. [2], are all fair with probability 1. Finally, we define and study equivalence between schedulers w.r.t. performance and correctness and prove that there exist fair probabilistic schedulers that are not equivalent w.r.t. to performance and others that are not equivalent w.r.t. correctness.
AB - We propose a novel, generic definition of probabilistic schedulers for population protocols. We then identify the consistent probabilistic schedulers, and prove that any consistent scheduler that assigns a non-zero probability to any transition i → j, where i and j are configurations satisfying i ≠ j, is fair with probability 1. This is a new theoretical framework that aims to simplify proving specific probabilistic schedulers fair. In this paper we propose two new schedulers, the State Scheduler and the Transition Function Scheduler. Both possess the significant capability of being protocol-aware, i.e. they can assign transition probabilities based on information concerning the underlying protocol. By using our framework we prove that the proposed schedulers, and also the Random Scheduler that was defined by Angluin et al. [2], are all fair with probability 1. Finally, we define and study equivalence between schedulers w.r.t. performance and correctness and prove that there exist fair probabilistic schedulers that are not equivalent w.r.t. to performance and others that are not equivalent w.r.t. correctness.
KW - Communicating automata
KW - Fair scheduler
KW - Fairness
KW - Population protocol
KW - Probabilistic scheduler
KW - Sensor network
UR - https://www.scopus.com/pages/publications/72749095017
U2 - 10.1007/978-3-642-10877-8_5
DO - 10.1007/978-3-642-10877-8_5
M3 - Conference contribution
AN - SCOPUS:72749095017
SN - 3642108768
SN - 9783642108761
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 33
EP - 47
BT - Principles of Distributed Systems - 13th International Conference, OPODIS 2009, Proceedings
T2 - 13th International Conference on Principles of Distributed Systems, OPODIS 2009
Y2 - 15 December 2009 through 18 December 2009
ER -