scholarly journals Sets of integers with no large sum-free subset

2014 ◽  
Vol 180 (2) ◽  
pp. 621-652 ◽  
Author(s):  
Sean Eberhard ◽  
Ben Green ◽  
Freddie Manners
Keyword(s):  
Free Subset

scholarly journals Functional identities on upper triangular matrix rings

2020 ◽  
Vol 18 (1) ◽  
pp. 182-193
Author(s):  
He Yuan ◽  
Liangyun Chen
Keyword(s):  
Triangular Matrix ◽  
Matrix Rings ◽  
Unital Ring ◽  
Functional Identities ◽  
Upper Triangular Matrix ◽  
Free Subset

Abstract Let R be a subset of a unital ring Q such that 0 ∈ R. Let us fix an element t ∈ Q. If R is a (t; d)-free subset of Q, then Tn(R) is a (t′; d)-free subset of Tn(Q), where t′ ∈ Tn(Q), $\begin{array}{} t_{ll}' \end{array} $ = t, l = 1, 2, …, n, for any n ∈ N.

A Relational Encoding for a Clash-Free Subset of ASMs

2016 ◽  
pp. 237-243 ◽  
Author(s):  
Gerhard Schellhorn ◽  
Gidon Ernst ◽  
Jörg Pfähler ◽  
Wolfgang Reif
Keyword(s):  
Relational Encoding ◽  
Free Subset

On zero-free subset sums

1996 ◽  
Vol 78 (2) ◽  
pp. 143-152 ◽  
Author(s):  
Yahya Hamidoune ◽  
Gilles Zémor
Keyword(s):  
Subset Sums ◽  
Free Subset

The equal-sum-free subset problem

2020 ◽  
Vol 86 (12) ◽  
pp. 73-79
Author(s):  
Gábor Bacsó ◽  
Zsolt Tuza
Keyword(s):  
Free Subset

Quasirandom Groups

2008 ◽  
Vol 17 (3) ◽  
pp. 363-387 ◽  
Author(s):  
W. T. GOWERS
Keyword(s):  
Finite Group ◽  
Sufficient Condition ◽  
Large Product ◽  
Simple Sufficient Condition ◽  
Free Subset

Babai and Sós have asked whether there exists a constant c > 0 such that every finite group G has a product-free subset of size at least c|G|: that is, a subset X that does not contain three elements x, y and z with xy = z. In this paper we show that the answer is no. Moreover, we give a simple sufficient condition for a group not to have any large product-free subset.

A partial evaluator for the untyped lambda-calculus

1991 ◽  
Vol 1 (1) ◽  
pp. 21-69 ◽  
Author(s):  
Carsten K. Gomard ◽  
Neil D. Jones
Keyword(s):  
Input Data ◽  
Partial Evaluation ◽  
Lambda Calculus ◽  
Higher Order ◽  
Residual Program ◽  
Source Program ◽  
Point Operator ◽  
Free Subset ◽  
Residual Code ◽  
Lambda Expression

AbstractThis article describes theoretical and practical aspects of an implemented self-applicable partial evaluator for the untyped lambda-calculus with constants and a fixed point operator. To the best of our knowledge, it is the first partial evaluator that is simultaneously higher-order, non-trivial, and self-applicable.Partial evaluation produces aresidual programfrom a source program and some of its input data. When given the remaining input data the residual program yields the same result that the source program would when given all its input data. Our partial evaluator produces a residual lambda-expression given a source lambda-expression and the values of some of its free variables. By self-application, the partial evaluator can be used to compile and to generate stand-alone compilers from a denotational or interpretive specification of a programming language.An essential component in our self-applicable partial evaluator is the use of explicitbinding time information.We use this to annotate the source program, marking asresidualthe parts for which residual code is to be generated and marking aseliminablethe parts that can be evaluated using only the data that is known during partial evaluation. We give a simple criterion,well-annotatedness,that can be used to check that the partial evaluator can handle the annotated higher-order programs without committing errors.Our partial evaluator is simple, is implemented in a side-effect free subset of Scheme, and has been used to compile and to generate compilers and a compiler generator. In this article we examine two machine-generated compilers and find that their structures are surprisingly natural.

scholarly journals Symbolic execution for a clash-free subset of ASMs

2018 ◽  
Vol 158 ◽  
pp. 21-40 ◽  
Author(s):  
Gerhard Schellhorn ◽  
Gidon Ernst ◽  
Jörg Pfähler ◽  
Stefan Bodenmüller ◽  
Wolfgang Reif
Keyword(s):  
Symbolic Execution ◽  
Free Subset

scholarly journals Subsums of a Zero-sum Free Subset of an Abelian Group

10.37236/840 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Weidong Gao ◽  
Yuanlin Li ◽  
Jiangtao Peng ◽  
Fang Sun
Keyword(s):  
Abelian Group ◽  
Lower Bound ◽  
Cyclic Group ◽  
Open Problem ◽  
Nonempty Subset ◽  
Finite Abelian Group ◽  
Positive Answer ◽  
Free Subset ◽  
Zero Sum ◽  
G 28

Let $G$ be an additive finite abelian group and $S \subset G$ a subset. Let f$(S)$ denote the number of nonzero group elements which can be expressed as a sum of a nonempty subset of $S$. It is proved that if $|S|=6$ and there are no subsets of $S$ with sum zero, then f$(S)\geq 19$. Obviously, this lower bound is best possible, and thus this result gives a positive answer to an open problem proposed by R.B. Eggleton and P. Erdős in 1972. As a consequence, we prove that any zero-sum free sequence $S$ over a cyclic group $G$ of length $|S| \ge {6|G|+28\over19}$ contains some element with multiplicity at least ${6|S|-|G|+1\over17}$.

scholarly journals Aliasing Models for Mobile Objects

1999 ◽  
Vol 6 (44) ◽  
Author(s):  
Uwe Nestmann ◽  
Hans Hüttel ◽  
Josva Kleist ◽  
Massimo Merro
Keyword(s):  
Programming Language ◽  
Type System ◽  
Object Oriented ◽  
Object Oriented Programming ◽  
Distributed Object ◽  
Mobile Objects ◽  
The Creation ◽  
Free Subset ◽  
Object Migration ◽  
Oriented Programming Language

In Obliq, a lexically scoped, distributed, object-oriented programming language, object migration was suggested as the creation of a copy of an object's state at the target site, followed by turning the object itself into an alias, also called surrogate, for the remote copy. We consider the creation of object surrogates as an abstraction of the above-mentioned style of migration. We introduce Øjeblik, a typed distribution-free subset of Obliq, and provide four different configuration-style semantics, which only differ in the respective aliasing model. We show that two of the semantics, one of which matches Obliq's implementation, render migration unsafe, while our new proposal allows for safe migration at least for a large class of program contexts. In addition, we propose a type system that allows a programmer to statically guarantee that programs belong to that class. Our work suggests a straightforward repair of Obliq's aliasing model.

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