Gasarch, William I.
Overview
Works:  27 works in 54 publications in 1 language and 289 library holdings 

Roles:  Author 
Classifications:  QA267.7, 511.35 
Publication Timeline
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Most widely held works by
William I Gasarch
Bounded queries in recursion theory by
William I Gasarch(
Book
)
10 editions published between 1998 and 1999 in English and Undetermined and held by 155 WorldCat member libraries worldwide
10 editions published between 1998 and 1999 in English and Undetermined and held by 155 WorldCat member libraries worldwide
Finding isolated cliques by queries an approach to fault diagnosis with many faults(
)
1 edition published in 2005 in English and held by 16 WorldCat member libraries worldwide
1 edition published in 2005 in English and held by 16 WorldCat member libraries worldwide
The communication complexity of the ExactN Problem revisited(
)
1 edition published in 2005 in English and held by 16 WorldCat member libraries worldwide
1 edition published in 2005 in English and held by 16 WorldCat member libraries worldwide
Learning via queries by
William I Gasarch(
Book
)
4 editions published between 1988 and 1990 in English and held by 13 WorldCat member libraries worldwide
Abstract: "We prove that the set of all recursive functions cannot be inferred using firstorder 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 [+, <]
4 editions published between 1988 and 1990 in English and held by 13 WorldCat member libraries worldwide
Abstract: "We prove that the set of all recursive functions cannot be inferred using firstorder 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
)
3 editions published in 1990 in English and held by 7 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 complexitytheoretic and recursiontheoretic  of characteristic vector terseness, which ask whether the answers to many membership queries to a hard set can be checked with fewer queries."
3 editions published in 1990 in English and held by 7 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 complexitytheoretic and recursiontheoretic  of characteristic vector terseness, which ask whether the answers to many membership queries to a hard set can be checked with fewer queries."
Recursiontheoretic properties of minimal honest polynomial degrees by
William I Gasarch(
Book
)
3 editions published in 1987 in English and held by 6 WorldCat member libraries worldwide
3 editions published in 1987 in English and held by 6 WorldCat member libraries worldwide
Training sequences by
Dana Angluin(
Book
)
2 editions published in 1987 in English and held by 6 WorldCat member libraries worldwide
2 editions published in 1987 in English and held by 6 WorldCat member libraries worldwide
Nondeterministic bounded query reducibilities by
Richard Beigel(
Book
)
2 editions published in 1987 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1987 in English and held by 5 WorldCat member libraries worldwide
Cheatable, pterse, and psuperterse sets by
Amihood Amir(
Book
)
2 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
Embedding the three element chain into the turing degrees : an exposition by
William I Gasarch(
Book
)
2 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
The complexity of optimization problems related to partition by
William I Gasarch(
Book
)
2 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
Applications of binary search to recursive graph theory by
Richard Beigel(
Book
)
2 editions published in 1987 in English and held by 5 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."
2 editions published in 1987 in English and held by 5 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."
The existence of matchings for recursive and highly recursive bipartite graphs by
William I Gasarch(
Book
)
2 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
Complexity issues in skeletal automata by Leona F Fass(
Book
)
2 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
Supportive and parallelsupportive sets by
Richard Beigel(
Book
)
2 editions published in 1987 in English and held by 5 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 parallelsupportive 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 parallelsupportive, all semirecursive sets are supportive and parallelsupportive, 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 parallelsupportive. We also show that the jump of every Turing degree contains a set that is not parallel supportive."
2 editions published in 1987 in English and held by 5 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 parallelsupportive 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 parallelsupportive, all semirecursive sets are supportive and parallelsupportive, 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 parallelsupportive. 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."
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."
Polynomial terse sets by
Amihood Amir(
Book
)
2 editions published in 1987 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1987 in English and held by 4 WorldCat member libraries worldwide
Selection problems via kary 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 kary queries are used instead. We show (a) 2ary queries ara [sic] no better than comparisons, (b) 3ary boolean queries are no better than 2ary queries when looking for maximum. Other results about kary boolean queries and ksorters are also examined."
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 kary queries are used instead. We show (a) 2ary queries ara [sic] no better than comparisons, (b) 3ary boolean queries are no better than 2ary queries when looking for maximum. Other results about kary boolean queries and ksorters are also examined."
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
1 edition published in 1988 in English and held by 4 WorldCat member libraries worldwide
Learning concepts from subconcepts by
William I Gasarch(
Book
)
2 editions published in 1986 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1986 in English and held by 3 WorldCat member libraries worldwide
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Associated Subjects
Artificial intelligence Computational complexity Computer science Computer scienceMathematics Decidability (Mathematical logic) Graph theoryData processing Inference Information theory Iterative methods (Mathematics) Machine learning Machine theory Matching theory Mathematical optimization Mathematics Operator theory Parallel programming (Computer science) Partitions (Mathematics) Recursion theory Recursive functions Set theory Turing machines