# Beigel, Richard

Overview
Works: 39 works in 58 publications in 4 languages and 504 library holdings QA267.3, 511.3
Publication Timeline
1980 | |2010
Key
Publications about Richard Beigel
Publications by Richard Beigel
Most widely held works by Richard Beigel
The language of machines : an introduction to computability and formal languages by Robert W Floyd ( Book )
12 editions published between 1993 and 1994 in English and held by 316 WorldCat member libraries worldwide
Le Langage des machines : introduction à la calculabilité et aux langages formels by Robert W Floyd ( Book )
2 editions published in 1995 in French and held by 57 WorldCat member libraries worldwide
Die Sprache der Maschinen by Robert W Floyd ( Book )
3 editions published in 1996 in German and held by 49 WorldCat member libraries worldwide
Query-limited reducibilities by Richard Beigel ( Book )
4 editions published between 1987 and 1988 in English and held by 10 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
A relationship between difference hierarchies and relativized polynomial hierarchies by Richard Beigel ( Book )
2 editions published in 1991 in English and held by 4 WorldCat member libraries worldwide
Finally, we consider two ways of relativizing the bounded query class $P_{k-tt}[superscript]{NP}$: the restricted relativization $P_{k-tt}[superscript]{NP[superscript]{C}}$, and the full relativization $\left(P_{k-tt}[superscript]{NP}\right)[superscrip t]{C}$. If $C$ is NP-hard, then we show that the two relativizations are different unless $PH[superscript]{C}$ collapses
Nondeterministic bounded query reducibilities by Richard Beigel ( Book )
1 edition published in 1987 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."
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."
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."
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
Terse, superterse, and verbose sets by Richard Beigel ( Book )
1 edition published in 1987 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."
The language of machines : an introduction to computability and formal language by Robert W Floyd ( Book )
2 editions published in 1994 in English and held by 3 WorldCat member libraries worldwide
On the power of probabilistic polynomial time : P [to the NP(log) power is contained as a subclass within] PP by Richard Beigel ( Book )
1 edition published in 1989 in English and held by 2 WorldCat member libraries worldwide
Class notes on interactive proof systems ( Book )
1 edition published in 1993 in English and held by 2 WorldCat member libraries worldwide
Baroko na Kolínsku I. : společnost a kultura v letech 1650-1730 : (rané a vrcholné baroko) ( Book )
1 edition published in 2001 in Czech and held by 2 WorldCat member libraries worldwide
On ACC by Richard Beigel ( Book )
1 edition published in 1990 in English and held by 2 WorldCat member libraries worldwide
Abstract: "Building on work of Toda [7] and Allender [1], Yao [9] has shown that every language in ACC is accepted by a family of depth-2 probabilistic circuits with a symmetric gate at the root and AND gates of small fanin at the next level. We simplify Yao's proof, and improve one of Toda's underlying technical results."
Improved bounds on coherence and checkability by Richard Beigel ( Book )
1 edition published in 1990 in English and held by 2 WorldCat member libraries worldwide
PP is closed under intersection by Richard Beigel ( Book )
1 edition published in 1990 in English and held by 2 WorldCat member libraries worldwide
Abstract: "In his seminal paper on probabilistic Turing machines, Gill [Gil77] asked whether the class PP is closed under intersection and union. We give a positive answer to this question. In fact, PP is closed under polynomial-time multilinear reductions. In circuits, this allows us to combine several threshold gates into a single threshold gate, while increasing depth by only a constant. Consequences in complexity theory include definite collapse and plausible separation of certain query hierarchies over PP

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English (33)
German (3)
French (2)
Czech (1)
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