Non-deterministic Population Protocols
In this paper we show that, in terms of generated output languages, non-deterministic population protocols are strictly more powerful than deterministic ones. Analyzing the reason for this negative result, we propose two slightly enhanced models, in which non-deterministic population protocols can be exactly simulated by deterministic ones. First, we consider a model in which interactions are not only between couples of agents, but also between triples and in which non-uniform initial states are allowed. We generalize this transformation and we prove a general property for a model with interactions between any number of agents. Second, we simulate any non-deterministic population protocol by a deterministic one in a model where a configuration can have an empty output.
Non-deterministic and deterministic population protocols are then compared in terms of inclusion of their output languages, that is, in terms of solvability of problems. We present a transformation realizing this inclusion. It uses (again) the natural model with interactions of triples, but does not need non-uniform initial states. As before, this result is generalized for the natural model with interactions between any number of agents.
Note that the transformations in the paper apply to a whole class of non-deterministic population protocols (for a proposed model), in contrast with the transformations proposed in previous works, which apply only to a specific sub-class of protocols (satisfying a so called “elasticity” condition).
KeywordsMobile Agent Output Sequence Population Protocol Deterministic Rule Presburger Arithmetic
Unable to display preview. Download preview PDF.
- 2.Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. In: PODC, pp. 290–299 (2004)Google Scholar
- 3.Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. DC 18(4), 235–253 (2006)Google Scholar
- 4.Angluin, D., Aspnes, J., Eisenstat, D., Ruppert, E.: The computational power of population protocols. DC 20(4), 279–304 (2007)Google Scholar
- 5.Angluin, D., Aspnes, J., Fischer, M.J., Jiang, H.: Self-stabilizing population protocols. TAAS 3(4) (2008)Google Scholar
- 6.Beauquier, J., Burman, J., Rosaz, L., Rozoy, B.: Non-deterministic population protocols (extended version). Technical Report hal-00736261, INRIA (2012)Google Scholar
- 8.Herman, T.: Adaptivity through Distributed Convergence. Ph.D. Thesis. University of Texas at Austin (1991)Google Scholar
- 9.Rabin, M.O., Scott, D.: Finite automata and their decision problems 3(2), 114 (1959)Google Scholar
- 10.Tel, G.: Introduction to Distributed Algorithms, 2nd edn. Cambridge University Press (2000)Google Scholar