Fraenkel, Aviezri S.
Overview
Works:  63 works in 169 publications in 2 languages and 305 library holdings 

Genres:  Conference papers and proceedings Academic theses 
Roles:  Author, Contributor, Editor 
Classifications:  QA269, 519.3 
Publication Timeline
.
Most widely held works by
Aviezri S Fraenkel
Combinatorial games by
Elwyn R Berlekamp(
)
3 editions published in 1991 in English and held by 45 WorldCat member libraries worldwide
3 editions published in 1991 in English and held by 45 WorldCat member libraries worldwide
Combinatorics and algorithms by
Aviezri S Fraenkel(
Book
)
9 editions published between 1989 and 1993 in English and held by 16 WorldCat member libraries worldwide
9 editions published between 1989 and 1993 in English and held by 16 WorldCat member libraries worldwide
Complexity of circuit intersection in graphs by
Aviezri S Fraenkel(
Book
)
10 editions published between 1991 and 1992 in English and German and held by 15 WorldCat member libraries worldwide
The case L = 2 of SBCI answers a question of Welsh, stemming from knot theory. The case L = 2 of NBCI, motivated by coding theory, has been shown to be polynomial for every graph by Frank."
10 editions published between 1991 and 1992 in English and German and held by 15 WorldCat member libraries worldwide
The case L = 2 of SBCI answers a question of Welsh, stemming from knot theory. The case L = 2 of NBCI, motivated by coding theory, has been shown to be polynomial for every graph by Frank."
Computing a perfect strategy for n x n chess requires time exponential in n by
Aviezri S Fraenkel(
Book
)
2 editions published in 1979 in English and held by 12 WorldCat member libraries worldwide
2 editions published in 1979 in English and held by 12 WorldCat member libraries worldwide
Complexity of games by
Aviezri S Fraenkel(
Book
)
5 editions published between 1981 and 1990 in English and held by 7 WorldCat member libraries worldwide
Abstract: "Nim, checkers, Go and chess belong to the same family of 2player full information 01 games without chance moves. Yet the strategy of Nim is very simple, that of chess seemingly very hard. Why?? Some of the reasons are explored and new theories are demonstrated by means of sample games of increasing complexity which span a bridge from Nim to chess."
5 editions published between 1981 and 1990 in English and held by 7 WorldCat member libraries worldwide
Abstract: "Nim, checkers, Go and chess belong to the same family of 2player full information 01 games without chance moves. Yet the strategy of Nim is very simple, that of chess seemingly very hard. Why?? Some of the reasons are explored and new theories are demonstrated by means of sample games of increasing complexity which span a bridge from Nim to chess."
Geodetic games on graphs by
Aviezri S Fraenkel(
Book
)
3 editions published in 1986 in English and Undetermined and held by 6 WorldCat member libraries worldwide
3 editions published in 1986 in English and Undetermined and held by 6 WorldCat member libraries worldwide
Epidemiography by
Aviezri S Fraenkel(
Book
)
6 editions published in 1987 in English and held by 6 WorldCat member libraries worldwide
6 editions published in 1987 in English and held by 6 WorldCat member libraries worldwide
Partizan octal games : partizan subtraction games by
Aviezri S Fraenkel(
Book
)
4 editions published between 1983 and 1986 in English and Undetermined and held by 6 WorldCat member libraries worldwide
4 editions published between 1983 and 1986 in English and Undetermined and held by 6 WorldCat member libraries worldwide
Properties of kWelter's game by N Duvdevani(
Book
)
2 editions published in 1986 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1986 in English and held by 5 WorldCat member libraries worldwide
Problems and results in complexity of combinatorial games by
Aviezri S Fraenkel(
Book
)
2 editions published in 1986 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1986 in English and held by 5 WorldCat member libraries worldwide
The number of fixed points of the majority rule by Z Agur(
Book
)
2 editions published in 1986 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1986 in English and held by 5 WorldCat member libraries worldwide
Generalized Wythoff arrays, shuffles and interspersions by
Aviezri S Fraenkel(
Book
)
3 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
Beatty sequences and Langford sequences by
Roger B Eggleton(
Book
)
3 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
Abstract: "Langford sequences and QuasiLangford sequences are defined and used to shed some light on disjoint covering systems and conversely. We also formulate two conjectures on QuasiLangford sequences, prove their equivalence, and show that they imply a 1973 conjecture on rational disjoint covering sequences."
3 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
Abstract: "Langford sequences and QuasiLangford sequences are defined and used to shed some light on disjoint covering systems and conversely. We also formulate two conjectures on QuasiLangford sequences, prove their equivalence, and show that they imply a 1973 conjecture on rational disjoint covering sequences."
Selected bibliography on combinatorial games and some related material by
Aviezri S Fraenkel(
Book
)
3 editions published in 1990 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1990 in English and held by 5 WorldCat member libraries worldwide
Iterated floor function, algebraic numbers, discrete chaos, Beatty subsequences, semigroups by
Aviezri S Fraenkel(
Book
)
3 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
(Beatty sequences have a large literature in combinatorics. They have also been used in nonperiodic tilings (quasicrystallography), periodic scheduling, computer vision (digital lines), and formal language theory.)."
3 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
(Beatty sequences have a large literature in combinatorics. They have also been used in nonperiodic tilings (quasicrystallography), periodic scheduling, computer vision (digital lines), and formal language theory.)."
Geography by
Aviezri S Fraenkel(
Book
)
4 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
Abstract: "Generalized Geography is an impartial twoperson game played on a digraph G = (V, A). In impartial Arc (Vertex) Geography, a token is initially placed on a special start vertex, and the players alternately move the token along unused arcs (vertices) of G. The player first unable to move loses and his opponent wins. The question of who wins these games IAG and IVG is known to be Pspacecomplete. Both impartial versions with two tokens on special start vertices are proved Pspace complete even for DAG's, but polynomial for directed trees. The partizan [sic] variations, PAG and PVG, with one token per player are Pspace complete even for degree restricted digraphs. They are NPhard for planar digraphs and DAG's, but polynomial for directed trees."
4 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
Abstract: "Generalized Geography is an impartial twoperson game played on a digraph G = (V, A). In impartial Arc (Vertex) Geography, a token is initially placed on a special start vertex, and the players alternately move the token along unused arcs (vertices) of G. The player first unable to move loses and his opponent wins. The question of who wins these games IAG and IVG is known to be Pspacecomplete. Both impartial versions with two tokens on special start vertices are proved Pspace complete even for DAG's, but polynomial for directed trees. The partizan [sic] variations, PAG and PVG, with one token per player are Pspace complete even for degree restricted digraphs. They are NPhard for planar digraphs and DAG's, but polynomial for directed trees."
Iterated Beatty functions by Alexander Barabash(
Book
)
3 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
Abstract: "We prove that an iterated Beatty function [formula] may be approximated by a sum of Beatty functions (without iteration) with a bounded error function X[subscript f], which can be represented as a composition [formula], where H(m) = ([m/q], [g₁ ..., [g[subcript n]m]), and 1/q, g₁ ..., g[subscript n] are real numbers, linearly independent over Z, and q is a positive integer ([x] denotes the fractional part of x); [psi][subscript f] is an integer function of a special type on the range of H. We use the properties of the wellstudied function H to derive many properties of X[subscript f], such as the fact that it has asymptotic frequencies, is not pseudorandom, yet is strongly aperiodic."
3 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
Abstract: "We prove that an iterated Beatty function [formula] may be approximated by a sum of Beatty functions (without iteration) with a bounded error function X[subscript f], which can be represented as a composition [formula], where H(m) = ([m/q], [g₁ ..., [g[subcript n]m]), and 1/q, g₁ ..., g[subscript n] are real numbers, linearly independent over Z, and q is a positive integer ([x] denotes the fractional part of x); [psi][subscript f] is an integer function of a special type on the range of H. We use the properties of the wellstudied function H to derive many properties of X[subscript f], such as the fact that it has asymptotic frequencies, is not pseudorandom, yet is strongly aperiodic."
Bidirectional Huffman coding by
Aviezri S Fraenkel(
Book
)
3 editions published in 1987 in English and Undetermined and held by 5 WorldCat member libraries worldwide
3 editions published in 1987 in English and Undetermined and held by 5 WorldCat member libraries worldwide
Deexponentializing complex computational mathematical problems using physical or biological systems by
Aviezri S Fraenkel(
Book
)
3 editions published in 1990 in English and held by 5 WorldCat member libraries worldwide
Abstract: "Many interesting mathematical problems are computationally intractable within the Turing machine model  yet decidable. Approximation methods, randomness, parallelization, imitation of Nature (genetic algorithms, neural networks), even tampering with Nature (molecular computers) have been proposed to cope with intractabilities. These remedies appear to operate within the basic Turing machine model and normally alleviate the intractabilities only slightly. It is suggested to use the basic physical or biological systems themselves  rather than imitations or models thereof  as 'black box' algorithms to solve intractable problems within reasonable time."
3 editions published in 1990 in English and held by 5 WorldCat member libraries worldwide
Abstract: "Many interesting mathematical problems are computationally intractable within the Turing machine model  yet decidable. Approximation methods, randomness, parallelization, imitation of Nature (genetic algorithms, neural networks), even tampering with Nature (molecular computers) have been proposed to cope with intractabilities. These remedies appear to operate within the basic Turing machine model and normally alleviate the intractabilities only slightly. It is suggested to use the basic physical or biological systems themselves  rather than imitations or models thereof  as 'black box' algorithms to solve intractable problems within reasonable time."
Information retrieval from annotated texts with applications to hypertexts by
Aviezri S Fraenkel(
Book
)
2 editions published in 1995 in English and held by 4 WorldCat member libraries worldwide
Abstract: "Methods for the correct and efficient handling of annotations in a fulltext retrieval system are investigated, with applications to a Hypertext environment in which even the hyperlinks are considered as searchable annotations. The problem with annotations is that they cannot be treated as regular text, since this would disrupt proximity searches, but on the other hand, they cannot be ignored, as they may carry important information. Moreover, in some cases, a user may wish to restrict a search to prespecified subsets of annotations. We suggest a new way of indexing the terms of the database to overcome the above dilemma."
2 editions published in 1995 in English and held by 4 WorldCat member libraries worldwide
Abstract: "Methods for the correct and efficient handling of annotations in a fulltext retrieval system are investigated, with applications to a Hypertext environment in which even the hyperlinks are considered as searchable annotations. The problem with annotations is that they cannot be treated as regular text, since this would disrupt proximity searches, but on the other hand, they cannot be ignored, as they may carry important information. Moreover, in some cases, a user may wish to restrict a search to prespecified subsets of annotations. We suggest a new way of indexing the terms of the database to overcome the above dilemma."
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Associated Subjects
Algebraic number theory Algorithms Binary system (Mathematics) Coding theory Combinatorial analysis Combinatorial analysisData processing Combinatorial optimization Computational complexity Computer chess Computer games Database searching Dynamic programming Electronic data processing Functions Game theory Game theoryData processing Geography Graph theory Hypertext systems Indexing Information retrieval Iterative methods (Mathematics) Mekhon Ṿaitsman lemadaʻ NPcomplete problems Sequences (Mathematics)
Alternative Names
Aviezri Fraenkel
Aviezri Fraenkel israelischer Mathematiker
Aviezri Fraenkel mathematician
Aviezri Fraenkel wiskundige uit Israël
Aviezri Frankel
Frenkel Aviezri S. 1929....
Prenqel ʾAbiyʿezriy 1929....
Френкель, Авиэзри израильский математик
אביעזרי פרנקל מחלוצי מדעי המחשב בישראל, פרופסור למתמטיקה במכון ויצמן למדע, הוגה פרויקט השו"ת, ממקימי המחלקה למתמטיקה ולמדעי
המחשב באוניברסיטת בראילן ומדוגלי השילוב בין מדע לתורה
פרנקל אביעזרי 1929....
アビエズリ・フレンケル
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