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25th Annual Symposium on Foundations of Computer Science (FOCS 1984)
Singer Island, FL
October 24October 26
ISBN: 081860591X
ASCII Text  x  
A.G. Greenberg, A. Weiss, "A Lower Bound For Probabilistic Algorithms For Finite State Machines," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 323331, 25th Annual Symposium on Foundations of Computer Science (FOCS 1984), 1984.  
BibTex  x  
@article{ 10.1109/SFCS.1984.715932, author = {A.G. Greenberg and A. Weiss}, title = {A Lower Bound For Probabilistic Algorithms For Finite State Machines}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {1984}, isbn = {081860591X}, pages = {323331}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.1984.715932}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  A Lower Bound For Probabilistic Algorithms For Finite State Machines SN  081860591X SP323 EP331 A1  A.G. Greenberg, A1  A. Weiss, PY  1984 VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
Freivalds recently reported a construction of a 2way probabilistic finite automaton M that recognizes the set {a/sup m/b /sup m/ : m /spl ges/ 1} with arbitrarily small probability of error. This result implies that probabilistic machines of this type are more powerful than their deterministic, nondeterministic, and alternating counterparts. Freivalds' construction has a negative feature: the automation M runs in /spl Omega/ (2/sup n/2/n) expected time in the worst case on inputs of length n. We show that it is impossible to do significantly better. Specifically, no 2way probabilistic finite automaton that runs in n/sup O (1)/ expected time recognizes {a/sup m/b/sup m/ : m /spl ges/ 1} with probability of error bounded away from 1/2. In passing we derive results on the densities of regular sets, the fine structure of Freivalds' construction, and the behavior of random walks controlled by Markov chains.
Citation:
A.G. Greenberg, A. Weiss, "A Lower Bound For Probabilistic Algorithms For Finite State Machines," focs, pp.323331, 25th Annual Symposium on Foundations of Computer Science (FOCS 1984), 1984
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