Abstract
The Ulam-Rényi game is a classical model for the problem of determining the minimum number of queries to find an unknown number in a finite set when up to a finite number of the answers may be erroneous/mendacious. In the variant considered in this paper, questions with q many possible answers are allowed, with q fixed and known beforehand; further, lies are constrained by a weighted bipartite graph (the “channel”). We provide a tight asymptotic estimate for the number of questions needed to solve the problem. Our results are constructive, and the appropriate searching strategies are actually provided. As an extra bonus, all our strategies use the minimum amount of adaptiveness: they ask a first batch of nonadaptive questions, and then, only depending on the answers to these questions, they ask a second nonadaptive batch.
This work was partially supported by INTAS 00-738
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
Berlekamp, E.R.: Block coding for the binary symmetric channel with noiseless, delayless feedback. In: Mann, H.B. (ed.) Error-correcting Codes, pp. 61–88. Wiley, New York (1968)
Cicalese, F., Deppe, C.: Quasi-Perfect Minimally Adaptive q-ary Search with Unreliable Tests. In: Ibaraki, T., Katoh, N., Ono, H. (eds.) ISAAC 2003. LNCS, vol. 2906, pp. 527–536. Springer, Heidelberg (2003)
Cicalese, F., Deppe, C.: Q-ary Ulam-Rényi game with constrained lies. In: Ahlswede, R., et al. (eds.) General Theory of Information Transfer and Combinatorics, Shannon Foundation Publishers (2004) (to appear)
Cicalese, F., Mundici, D.: Optimal binary search with two unreliable tests and minimum adaptiveness. In: Nešetřil, J. (ed.) ESA 1999. LNCS, vol. 1643, pp. 257–266. Springer, Heidelberg (1999)
Cicalese, F., Mundici, D.: Perfect two fault-tolerant search with minimum adaptiveness. Advances in Applied Mathematics 25, 65–101 (2000)
Cicalese, F., Mundici, D., Vaccaro, U.: Least adaptive optimal search with unreliable tests. Theoretical Computer Science 270, 877–893 (2001)
Cicalese, F., Mundici, D., Vaccaro, U.: Rota-Metropolis cubic logic and Ulam- Rényi games. In: Crapo, H., Senato, D. (eds.) Algebraic Combinatorics and Computer Science – A Tribute to Giancarlo Rota, pp. 197–244. Springer, Heidelberg (2001)
Deppe, C.: Searching with lies and coding with feedback. In: Search and Communication Complexity, Information Theory in Mathematics. Series of Bolyai Studies. Springer, Heidelberg (to appear)
Dumitriu, I., Spencer, J.: The Liar Game over an Arbitrary Channel (2003) (to appear)
Pelc, A.: Searching games with errors – fifty years of coping with liars. Theoret. Comput. Sci. 270, 71–109 (2002)
Rényi, A.: On a problem of information theory. MTA Mat. Kut. Int. Kozl. 6B, 505–516 (1961)
Ulam, S.M.: Adventures of a Mathematician. Scribner’s, New York (1976)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cicalese, F., Deppe, C., Mundici, D. (2004). Q-Ary Ulam-Rényi Game with Weighted Constrained Lies. In: Chwa, KY., Munro, J.I.J. (eds) Computing and Combinatorics. COCOON 2004. Lecture Notes in Computer Science, vol 3106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27798-9_11
Download citation
DOI: https://doi.org/10.1007/978-3-540-27798-9_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22856-1
Online ISBN: 978-3-540-27798-9
eBook Packages: Springer Book Archive