Solution of Ulam's problem on searching with a lie
Journal of Combinatorial Theory Series A
Search problems
Ulam's searching game with two lies
Journal of Combinatorial Theory Series A
Ulam's searching game with a fixed number of lies
Theoretical Computer Science
Surveys in combinatorics, 1995
Searching games with errors---fifty years of coping with liars
Theoretical Computer Science
Least adaptive optimal search with unreliable tests
Theoretical Computer Science
Adaptive search engines as discovery games: an evolutionary approach
Proceedings of the 6th International Conference on Advances in Mobile Computing and Multimedia
Community Adaptive Search Engines
International Journal of Advanced Intelligence Paradigms
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We consider the problem of finding the minimal number Ll(M) of binary questions needed to find an unknown element of a set of cardinality M with a sequential strategy if at most l of the answers are lies. Obviously, in the case l = 0 ⌈ log M ⌉ questions are needed. Thus, one more question is necessary if the number of elements is doubled. We show that for every fixed l and sufficiently large M, then Ll(2M) ≤ Ll(M) + 2 and moreover Ll(3/2M) ≤ Ll(M)+ 1. These bounds are sharp in infinitely many cases. As a consequence, at most one question more than the information theoretic lower bound is needed to successfully find the unknown number. One of our strategies uses the minimum amount of adaptiveness during the search process.