Beigel, Richard
Overview
Works:  31 works in 52 publications in 3 languages and 491 library holdings 

Roles:  Author 
Classifications:  QA267.3, 511.3 
Publication Timeline
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Most widely held works by
Richard Beigel
The language of machines : an introduction to computability and formal languages by
Robert W Floyd(
Book
)
13 editions published between 1993 and 1994 in English and held by 325 WorldCat member libraries worldwide
13 editions published between 1993 and 1994 in English and held by 325 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
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 48 WorldCat member libraries worldwide
3 editions published in 1996 in German and held by 48 WorldCat member libraries worldwide
Querylimited reducibilities by
Richard Beigel(
Book
)
5 editions published between 1987 and 1988 in English and held by 11 WorldCat member libraries worldwide
5 editions published between 1987 and 1988 in English and held by 11 WorldCat member libraries worldwide
A relationship between difference hierarchies and relativized polynomial hierarchies by
Richard Beigel(
Book
)
3 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
Chang and Kadin have shown that if the difference hierarchy over NP collapses to level $k$, then the polynomial hierarchy (PH) is equal to the $k$th level of the difference hierarchy over $\Sigma_{2}[superscript]{p}$. We simplify their proof and obtain a slightly stronger conclusion: If the difference hierarchy over NP collapses to level $k$, then PH = $\left(P_{(k1)tt}[superscript]{NP}\right)[supers cript]{NP}$. We also extend the result to classes other than NP: For any class $C$ that has $\leq_{m}[superscript]{p}$complete sets and is closed under $\leq_{conj}[superscript]{p}$ and $\leq_{m}[superscript]{NP}$reductions, if the difference hierarchy over $C$ collapses to level $k$, then $PH[superscript]{C} = $\left(P_{(k1)tt}[superscript]{NP}\right)[supers cript]{C}$. Then we show that the exact counting class $C_{=}P$ is closed under $\leq_{disj}[superscript]{p}$ and $\leq_{m}[superscript]{coNP}$reductions. Consequently, if the difference hierarchy over $C_{=}P$ collapses to level $k$ then $PH[superscript]{PP}$ is equal to $\left(P_{(k1)tt}[superscript]{NP}\right)[supers cript]{PP}$. In contrast, the difference hierarchy over the closely related class PP is known to collapse
3 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
Chang and Kadin have shown that if the difference hierarchy over NP collapses to level $k$, then the polynomial hierarchy (PH) is equal to the $k$th level of the difference hierarchy over $\Sigma_{2}[superscript]{p}$. We simplify their proof and obtain a slightly stronger conclusion: If the difference hierarchy over NP collapses to level $k$, then PH = $\left(P_{(k1)tt}[superscript]{NP}\right)[supers cript]{NP}$. We also extend the result to classes other than NP: For any class $C$ that has $\leq_{m}[superscript]{p}$complete sets and is closed under $\leq_{conj}[superscript]{p}$ and $\leq_{m}[superscript]{NP}$reductions, if the difference hierarchy over $C$ collapses to level $k$, then $PH[superscript]{C} = $\left(P_{(k1)tt}[superscript]{NP}\right)[supers cript]{C}$. Then we show that the exact counting class $C_{=}P$ is closed under $\leq_{disj}[superscript]{p}$ and $\leq_{m}[superscript]{coNP}$reductions. Consequently, if the difference hierarchy over $C_{=}P$ collapses to level $k$ then $PH[superscript]{PP}$ is equal to $\left(P_{(k1)tt}[superscript]{NP}\right)[supers cript]{PP}$. In contrast, the difference hierarchy over the closely related class PP is known to collapse
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
Terse, superterse, and verbose sets by
Richard Beigel(
Book
)
1 edition published in 1987 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 1987 in English and held by 4 WorldCat member libraries worldwide
Nondeterministic bounded query reducibilities by
Richard Beigel(
Book
)
1 edition published in 1987 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 1987 in English and held by 4 WorldCat member libraries worldwide
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."
Cheatable, pterse, and psuperterse sets by
Amihood Amir(
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
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
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
1 edition published in 1993 in English and held by 2 WorldCat member libraries worldwide
Communicating with lowdiffraction lasers and mirrors by
Richard Beigel(
Book
)
1 edition published in 1992 in English and held by 2 WorldCat member libraries worldwide
Using slightly more complicated optical devices, such as beam splitters, we design a 'light guide, ' which allows simultaneous broadcasts, subject only to the limitations of light sensors. In particular, the light guide can perform single broadcasts. Given accurate enough clocks, it can perform arbitrary permutations."
1 edition published in 1992 in English and held by 2 WorldCat member libraries worldwide
Using slightly more complicated optical devices, such as beam splitters, we design a 'light guide, ' which allows simultaneous broadcasts, subject only to the limitations of light sensors. In particular, the light guide can perform single broadcasts. Given accurate enough clocks, it can perform arbitrary permutations."
The language of machines : an introduction to compatibility and formal languages(
Book
)
1 edition published in 1994 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1994 in English and held by 2 WorldCat member libraries worldwide
The language of machines : an introduction to computability and formal languages : instructor's manual to accompany by
Richard Beigel(
Book
)
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
NPhard sets are psuperterse unless R = NP by
Richard Beigel(
Book
)
1 edition published in 1988 in English and held by 1 WorldCat member library worldwide
1 edition published in 1988 in English and held by 1 WorldCat member library worldwide
The mapmaker's dilemma by
Richard Beigel(
Book
)
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
Unbounded searching algorithms by
Richard Beigel(
Book
)
1 edition published in 1988 in English and held by 1 WorldCat member library worldwide
Abstract: "The unbounded search problem was posed by Bentley and Yao. It is the problem of finding a key in a linearly ordered unbounded table, with the proviso that the number of comparisons is to be minimized. We show that Bentley and Yao's lower bound is essentially optimal, and we prove some new upper bounds for the unbounded search problem. We show how to solve this problem in parallel as well."
1 edition published in 1988 in English and held by 1 WorldCat member library worldwide
Abstract: "The unbounded search problem was posed by Bentley and Yao. It is the problem of finding a key in a linearly ordered unbounded table, with the proviso that the number of comparisons is to be minimized. We show that Bentley and Yao's lower bound is essentially optimal, and we prove some new upper bounds for the unbounded search problem. We show how to solve this problem in parallel as well."
Irrationality without number theory by
Richard Beigel(
Book
)
1 edition published in 1988 in English and held by 1 WorldCat member library worldwide
Abstract: "For all positive integers k and t, we show that k[superscript 1/t] is either a positive integer or an irrational number. Unlike classical methods for proving this wellknown result, our proof does not use any number theory. Instead, our proof depends on very basic inequalities."
1 edition published in 1988 in English and held by 1 WorldCat member library worldwide
Abstract: "For all positive integers k and t, we show that k[superscript 1/t] is either a positive integer or an irrational number. Unlike classical methods for proving this wellknown result, our proof does not use any number theory. Instead, our proof depends on very basic inequalities."
An efficient algorithm for dynamic text indexing by
Ming Gu(
)
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
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Algorithms CartographyComputer programs Computable functions Computational complexity Computer algorithms Formal languages Graph theoryData processing Machine theory MapsComputer programs Number theory Optical data processing Parallel programming (Computer science) Polynomials Programming languages (Electronic computers) Proof theory Recursion theory Recursive functions Search theory Set theory Turing machines