Results 1  10
of
616,293
SHORT PROOF
, 2009
"... Abstract. It is shown that for every α, where α∈[0, 1/2], there exists an αrigid transformation whose spectrum has Lebesgue component. This answers the question posed by Klemes and Reinhold in [7]. We apply a certain correspondence between weak limits of powers of a transformation and its skew prod ..."
Abstract
 Add to MetaCart
Abstract. It is shown that for every α, where α∈[0, 1/2], there exists an αrigid transformation whose spectrum has Lebesgue component. This answers the question posed by Klemes and Reinhold in [7]. We apply a certain correspondence between weak limits of powers of a transformation and its skew products.
Short Proofs For Interval Digraphs
 Discrete Math
, 1996
"... . We give short proofs of the adjacency matrix characterizations of interval digraphs and unit interval digraphs. 1. INTRODUCTION An intersection representation of a graph assigns each vertex a set so that vertices are adjacent if and only if the corresponding sets intersect. Beineke and Zamfirescu ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
. We give short proofs of the adjacency matrix characterizations of interval digraphs and unit interval digraphs. 1. INTRODUCTION An intersection representation of a graph assigns each vertex a set so that vertices are adjacent if and only if the corresponding sets intersect. Beineke
Short Proofs are Narrow  Resolution made Simple
 Journal of the ACM
, 2000
"... The width of a Resolution proof is de ned to be the maximal number of literals in any clause of the proof. In this paper we relate proof width to proof length (=size), in both general Resolution, and its treelike variant. The following consequences of these relations reveal width as a crucial " ..."
Abstract

Cited by 204 (14 self)
 Add to MetaCart
The width of a Resolution proof is de ned to be the maximal number of literals in any clause of the proof. In this paper we relate proof width to proof length (=size), in both general Resolution, and its treelike variant. The following consequences of these relations reveal width as a crucial
Short Proofs of Knowledge for Factoring
 in PKC 2000, Springer LNCS 1751
, 2000
"... . The aim of this paper is to design a proof of knowledge for the factorization of an integer n. We propose a statistical zeroknowledge protocol similar to proofs of knowledge of discrete logarithm a la Schnorr. The efficiency improvement in comparison with the previously known schemes can be compa ..."
Abstract

Cited by 14 (4 self)
 Add to MetaCart
. The aim of this paper is to design a proof of knowledge for the factorization of an integer n. We propose a statistical zeroknowledge protocol similar to proofs of knowledge of discrete logarithm a la Schnorr. The efficiency improvement in comparison with the previously known schemes can
Combinatorial PCPs with Short Proofs
, 2012
"... The PCP theorem (Arora et. al., J. ACM 45(1,3)) asserts the existence of proofs that can be verified by reading a very small part of the proof. Since the discovery of the theorem, there has been a considerable work on improving the theorem in terms of the length of the proofs, culminating in the con ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
The PCP theorem (Arora et. al., J. ACM 45(1,3)) asserts the existence of proofs that can be verified by reading a very small part of the proof. Since the discovery of the theorem, there has been a considerable work on improving the theorem in terms of the length of the proofs, culminating
Short proofs of strong normalization
"... Abstract. This paper presents simple, syntactic strong normalization proofs for the simplytyped λcalculus and the polymorphic λcalculus (system F) with the full set of logical connectives, and all the permutative reductions. The normalization proofs use translations of terms and types of λ→,∧,∨, ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. This paper presents simple, syntactic strong normalization proofs for the simplytyped λcalculus and the polymorphic λcalculus (system F) with the full set of logical connectives, and all the permutative reductions. The normalization proofs use translations of terms and types of λ
Short proofs for the determinant identities
 CoRR
, 2011
"... We study arithmetic proof systems Pc(F) and Pf (F) operating with arithmetic circuits and arithmetic formulas, respectively, and that prove polynomial identities over a field F. We establish a series of structural theorems about these proof systems, the main one stating that Pc(F) proofs can be bala ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
We study arithmetic proof systems Pc(F) and Pf (F) operating with arithmetic circuits and arithmetic formulas, respectively, and that prove polynomial identities over a field F. We establish a series of structural theorems about these proof systems, the main one stating that Pc(F) proofs can
Short proofs for MIU theorems
, 1998
"... We study the MIU formal system, characterizing all possible theorems. We propose an algorithm to prove that a given formula t is a theorem, and based on that algorithm we prove that the number of lines of a minimum line proof is O(max{n_u, logt}) and the number of symbols of a minimum line proof i ..."
Abstract
 Add to MetaCart
We study the MIU formal system, characterizing all possible theorems. We propose an algorithm to prove that a given formula t is a theorem, and based on that algorithm we prove that the number of lines of a minimum line proof is O(max{n_u, logt}) and the number of symbols of a minimum line proof
A short proof of the . . .
, 1996
"... Rook numbers of complementary boards are related by a reciprocity law. A complicated formula for this law has been known for about fifty years, but recently Gessel and the present author independently obtained a much more elegant formula, as a corollary of more general reciprocity theorems. Here, ..."
Abstract
 Add to MetaCart
, following a suggestion of Goldman, we provide a direct combinatorial proof of this new formula.
Short Proofs for Pythagorean Theorem
"... Abstract. The Pythagorean Theorem can be introduced to students during the middle school years. This theorem becomes increasingly important during the high school years. It is not enough to merely state the algebraic formula for the Pythagorean Theorem. Students need to see the geometric connections ..."
Abstract
 Add to MetaCart
Abstract. The Pythagorean Theorem can be introduced to students during the middle school years. This theorem becomes increasingly important during the high school years. It is not enough to merely state the algebraic formula for the Pythagorean Theorem. Students need to see the geometric connections as well. The teaching and learning of the Pythagorean Theorem can be enriched and enhanced through the use of dot paper, geoboards, paper folding, and computer technology, as well as many other instructional materials. Through the use of manipulatives and other educational resources, the Pythagorean Theorem can mean much more to students than just a2 = b2+ c2 and plugging numbers into the formula.
Results 1  10
of
616,293