Arithmetic Complexity of the Predicate Logics of Complete Arithmetic Theories

Author(s):  
Valeri Plisko
2019 ◽  
Vol 119 (6) ◽  
pp. 1206-1222 ◽  
Author(s):  
Camille Desrochers ◽  
Pierre-Majorique Léger ◽  
Marc Fredette ◽  
Seyedmohammadmahdi Mirhoseini ◽  
Sylvain Sénécal

Purpose Online grocery shopping possesses characteristics that can make it more difficult than regular online shopping. There are numerous buying decisions to make each shopping session, there are large ranges of product types to choose from and there is varied arithmetical complexity. The purpose of this paper is to examine how such characteristics influence the attitude of consumers toward online grocery shopping websites. Design/methodology/approach The authors hypothesized that the product type (search or experience product), the task arithmetic complexity, and the attention and cognitive load associated with browsing through product pictures have an effect on the attitude of online shoppers toward these websites. To test the hypotheses, 31 subjects participated in a within-subject laboratory experiment. Findings The results suggest that visual attention to product pictures has a positive effect on the attitude of online shoppers toward a website when they are shopping for experience goods, but that it has a negative effect on their attitude toward a website when the task arithmetic complexity is greater. They also suggest that the cognitive load associated with browsing through product pictures has a negative effect on the attitude of online shoppers toward a website when they are shopping for experience goods, and that greater cognitive load variation has a positive effect on their attitude toward a website when arithmetic task complexity is greater. Practical implications When designing online grocery websites, providing clear single unit quantities with pictures corresponding to the sales unit could help establish a clear baseline on which consumers can work out their quantity requirements. For decisions involving experience goods, product pictures may act as an important complementary information source and may even be more diagnostic than text description. Originality/value Results reinforce the relevance of enriching the study of self-reported measures of the user experience on e-commerce sites with automatic measures.


2001 ◽  
Vol 63 (3) ◽  
pp. 467-473 ◽  
Author(s):  
Edwin El Mahassni ◽  
Igor Shparlinski

We obtain lower bounds on the degrees of polynomials representing the Diffie-Hellman mapping (gx, gy) → gxy, where g is a primitive root of a finite field q of q elements. These bounds are exponential in terms of log q. In particular, these results can be used to obtain lower bounds on the parallel arithmetic complexity of breaking the Diffie-Hellman cryptosystem. The method is based on bounds of numbers of solutions of some polynomial equations.


2015 ◽  
Vol 25 (2) ◽  
Author(s):  
Sergey B. Gashkov

AbstractFor the linear Stirling transforms of both kinds, which are well-known in combinatorics, we obtain close to optimal estimates of the complexity of computation by vector addition chains and non-branching programs composed of arithmetic operations over real numbers. A relation between these problems and the Lagrange and Newton interpolation is discussed.


2012 ◽  
Vol 13 (3) ◽  
pp. 1-18 ◽  
Author(s):  
Bjørn Kjos-Hanssen ◽  
Frank Stephan ◽  
Jason Teutsch

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