Prefix search with a lie

The problem of performing a search procedure when some of the answers to queries may be erroneous has been recently investigated by many authors (see [3,4, 2, 11). One of the main questions in this domain was stated by S. M. Ulam [S]: what is the minimal number of yes-no queries sufficient to find an unknown object in an n-element set if at most one answer may be erroneous? This problem was first partly solved by Rivest et al. [3] and Spencer [4] who gave bounds for this minimal number of queries. The complete answer to Ulam’s question was given in Pelt [ 11. In the present paper we continue the study of search with one possible lie. However, instead of considering arbitrary yes-no queries (i.e., queries of the form x E A?, where A is any subset of the search space), we impose a natural restriction on the type of permitted questions. Our space of search is now the set of leaves of a full binary tree of height n, i.e., the set T, = (0, 1 }” of binary sequences of length iz. (The tree itself is often identified with the set of its leaves.) The permitted queries are exclusively those of the form: is the hidden leaf x in the subtree with a given prefix s, i.e., x E T:?, where