WorldCat Identities

Gasarch, William I.

Overview
Works: 30 works in 47 publications in 1 language and 276 library holdings
Roles: Creator
Classifications: QA267.7, 511.35
Publication Timeline
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Publications about  William I Gasarch Publications about William I Gasarch
Publications by  William I Gasarch Publications by William I Gasarch
Most widely held works by William I Gasarch
Bounded queries in recursion theory by William I Gasarch ( Book )
11 editions published between 1998 and 2013 in English and Undetermined and held by 147 WorldCat member libraries worldwide
Finding isolated cliques by queries an approach to fault diagnosis with many faults ( )
2 editions published in 2005 in English and held by 17 WorldCat member libraries worldwide
The communication complexity of the Exact-N Problem revisited ( )
2 editions published in 2005 in English and held by 17 WorldCat member libraries worldwide
Learning via queries by William I Gasarch ( Book )
3 editions published between 1988 and 1990 in English and held by 12 WorldCat member libraries worldwide
Abstract: "We prove that the set of all recursive functions cannot be inferred using first-order queries in the query language containing extra symbols [+, <]. The proof involves a new decidability result about Presburger arithmetic of independent interest: Given a formula [phi](A) in the language [+, <] that has all variables bound and ranging over the natural numbers, except for one free set variable A, one can pick one of [[psi](A), [not equal][psi](A)] that is true for an uncountable number of sets. We also show that the set of all primitive recursive functions cannot be inferred with a bounded number of mind changes, again using queries in [+, <]
On checking versus evaluation of multiple queries by William I Gasarch ( Book )
2 editions published in 1990 in English and held by 6 WorldCat member libraries worldwide
Abstract: "The distinction between computing answers and checking answers is fundamental to computational complexity theory, and is reflected in the relationship of NP to P. The plausibilty of computing the answers to many membership queries to a hard set with few queries is the subject of the theory of terseness. In this paper, we develop companion theories -- both complexity-theoretic and recursion-theoretic -- of characteristic vector terseness, which ask whether the answers to many membership queries to a hard set can be checked with fewer queries."
Recursion-theoretic properties of minimal honest polynomial degrees by William I Gasarch ( Book )
2 editions published in 1987 in English and held by 5 WorldCat member libraries worldwide
Training sequences by Dana Angluin ( Book )
1 edition published in 1987 in English and held by 5 WorldCat member libraries worldwide
Cheatable, p-terse, and p-superterse sets by Amihood Amir ( Book )
1 edition published in 1988 in English and held by 4 WorldCat member libraries worldwide
On the complexity of finding the chromatic number of a recursive graph II : the unbounded case by Richard Beigel ( Book )
1 edition published in 1988 in English and held by 4 WorldCat member libraries worldwide
The existence of matchings for recursive and highly recursive bipartite graphs by William I Gasarch ( Book )
1 edition published in 1988 in English and held by 4 WorldCat member libraries worldwide
Applications of binary search to recursive graph theory by Richard Beigel ( Book )
1 edition published in 1987 in English and held by 4 WorldCat member libraries worldwide
Abstract: "We classify functions in recursive graph theory in terms of how many queries to K (or ø'' or ø''') are required to compute them. We show that (1) binary search is optimal (in terms of the number of queries to K) for finding the chromatic number of a recursive graph; no set of Turing degree less than K will suffice, (2) determining if a recursive graph has a finite chromatic number is [sigma subscript 2]-complete, and (3) binary search is optimal (in terms of the number of queries to ø''') for finding the recursive chromatic number of a recursive graph; no set of Turing degree less than ø''' will suffice. Some of our results have analogues in terms of asking p questions, but some do not. In particular (p + 1)-ary search is not always optimal for finding the chromatic number of a recursive graph. All results are also true for highly recursive graphs."
Selection problems via k-ary queries by Katia Guimaraes ( Book )
1 edition published in 1990 in English and held by 4 WorldCat member libraries worldwide
Abstract: "Algorithms for selection problems are usually written with comparison as being the basic operation. We examine what happens if k-ary queries are used instead. We show (a) 2-ary queries ara [sic] no better than comparisons, (b) 3-ary boolean queries are no better than 2-ary queries when looking for maximum. Other results about k-ary boolean queries and k-sorters are also examined."
Embedding the three element chain into the turing degrees : an exposition by William I Gasarch ( Book )
1 edition published in 1988 in English and held by 4 WorldCat member libraries worldwide
Supportive and parallel-supportive sets by Richard Beigel ( Book )
1 edition published in 1987 in English and held by 4 WorldCat member libraries worldwide
Abstract: "Let A be an oracle. We say that A is supportive if we can solve more decision problems by making n+1 queries to A than we can solve by making only n queries to A. We say that A is parallel-supportive if we can solve more decision problems by making n+1 simultaneous queries to A than we can solve by making only n simultaneous queries to A. We conjecture that all nonrecursive sets are supportive. In [BGH87] we showed that the halting set is supportive and parallel supportive. In this paper we show that the jump of every set is supportive and parallel supportive, all generic sets are supportive and parallel-supportive, all semi-recursive sets are supportive and parallel-supportive, every Turing degree contains a set that is supportive and parallel supportive, and every r.e. Turing degree contains an r.e. set that is supportive and parallel-supportive. We also show that the jump of every Turing degree contains a set that is not parallel supportive."
Frequency computation and bounded queries by Richard Beigel ( Book )
1 edition published in 1993 in English and held by 4 WorldCat member libraries worldwide
Abstract: "For a set A and a number m let F[superscript A, subscript n](x₁ ..., x[subscript n]) = [subscript XA](x₁) ... [subscript XA](x[subscript n]). We study how hard it is to approximate this function in terms of the number of queries required. We obtain matching upper and lower bounds for the case A = K (the halting set), A semirecursive, and (assuming P [not equal] NP) A = SAT. Some of our bounds depend on functions from coding theory."
Nondeterministic bounded query reducibilities by Richard Beigel ( Book )
1 edition published in 1987 in English and held by 4 WorldCat member libraries worldwide
The complexity of optimization problems related to partition by William I Gasarch ( Book )
1 edition published in 1988 in English and held by 4 WorldCat member libraries worldwide
Complexity issues in skeletal automata by Leona F Fass ( Book )
1 edition published in 1988 in English and held by 4 WorldCat member libraries worldwide
Bounded query classes and the difference hierarchy by Richard Beigel ( Book )
1 edition published in 1987 in English and held by 3 WorldCat member libraries worldwide
Abstract: "Let A be any nonrecursive set. We define a hierarchy of sets (and a corresponding hierarchy of degrees) that are Turing reducible to A based on bounding the number of questions to A that an oracle machine can make. If A = K then our hierarchy of sets interleaves with the difference hierarchy on the r.e. sets in a logarithmic way; however, our hierarchy of degrees is a sub-hierarchy if the difference degrees."
[Seventh Annual Workshop on Computational Learning Theory (COLT) 1994] ( )
2 editions published in 1996 in English and held by 3 WorldCat member libraries worldwide
 
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Alternative Names
Gasarch, W. I.
Gasarch, William
Languages
English (36)
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