1994
DOI: 10.1002/malq.19940400209
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Effective Search Problems

Abstract: The task of computing a function F with the help of an oracle X can be viewed as a search problem where the cost measure is the number of queries to X. We ask for the minimal number that can be achieved by a suitable choice of X and call this quantity the query complezity of F. This concept is suggested by earlier work of Beigel, Gasarch, Gill, and Owings on "Bounded query classes". We introduce a fault tolerant version and relate it with Ulam's game. For many natural classes of functions F we obtain tight upp… Show more

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Cited by 17 publications
(4 citation statements)
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“…(This concept first appeared in a recursiontheoretic framework in [Bei87b]. Some very general theorems about EN(«) were proved in [KS94]. The name "enumerable" was coined in [CH89].)…”
Section: Definition 5 ([Bgg093]mentioning
confidence: 99%
See 1 more Smart Citation
“…(This concept first appeared in a recursiontheoretic framework in [Bei87b]. Some very general theorems about EN(«) were proved in [KS94]. The name "enumerable" was coined in [CH89].)…”
Section: Definition 5 ([Bgg093]mentioning
confidence: 99%
“…Several natural examples of functions have been classified under the query complexity measure [BGG093,BGK96a,Gas91,Kum92,KS94]. In this paper we investigate the complexity of the following sets: DEFINITION 1.…”
mentioning
confidence: 99%
“…ii. Kummer and Stephan [KS93a] have shown that for any nonrecursive set A there is a function T REE A k that can be computed with k queries to A that cannot be computed with k − 1 queries to any set. This will be used in two places (Notes 4.16 and 6.35) to slightly improve our results.…”
Section: Definition 42 F Amentioning
confidence: 99%
“…Traditional approximations are a special case of this, in which the set of candidates is the set of numbers in a given range. This kind of approximation has been called enumeration complexity, see [1,2,4,5,7,8,12,18]. Bill Gasarch suggested the natural question whether we can approximate the Kolmogorov function in this sense, or more precisely, how many values does a Turing machine need to output before it is guaranteed that one of the values is C(x).…”
Section: Introductionmentioning
confidence: 99%