Solution of Ulam's problem on searching with a lie
Journal of Combinatorial Theory Series A
Handbook of Coding Theory
The Two-Batch Liar Game over an Arbitrary Channel
SIAM Journal on Discrete Mathematics
The Rényi-Ulam pathological liar game with a fixed number of lies
Journal of Combinatorial Theory Series A
Searching with lies under error cost constraints
Discrete Applied Mathematics
Two batch search with lie cost
IEEE Transactions on Information Theory
Long nonbinary codes exceeding the Gilbert-Varshamov bound for any fixed distance
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Q-ary Rényi-Ulam pathological liar game with one lie
Discrete Applied Mathematics
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We consider an extension of the 2-person Renyi-Ulam liar game in which lies are governed by a channel C, a set of allowable lie strings of maximum length k. Carole selects x@?[n], and Paul makes t-ary queries to uniquely determine x. In each of q rounds, Paul weakly partitions [n]=A"0@?...@?A"t"-"1 and asks for a such that x@?A"a. Carole responds with some b, and if ab, then x accumulates a lie (a,b). Carole's string of lies for x must be in the channel C. Paul wins if he determines x within q rounds. We further restrict Paul to ask his questions in two off-line batches. We show that for a range of sizes of the second batch, the maximum size of the search space [n] for which Paul can guarantee finding the distinguished element is ~t^q^+^k/(E"k(C)(qk)) as q-~, where E"k(C) is the number of lie strings in C of maximum length k. This generalizes previous work of Dumitriu and Spencer, and of Ahlswede, Cicalese, and Deppe. We extend Paul's strategy to solve also the pathological liar variant, in a unified manner which gives the existence of asymptotically perfect two-batch adaptive codes for the channel C.