We consider the first order theory of (Z,+, <), also known as Presburger arithmetic. We prove a characterization of definable types in terms of prime models over realizations, which has a similar flavor to the Marker-Steinhorn Theorem of o-minimality. We also prove that a type over a model is definable if and only if it has a unique coheir to any elementary extension, which is a characterizatio...

Polynomial constraint-solving plays a prominent role in several areas of engineering and software verification. In particular, polynomial constraint solving has a long and successful history in the development of tools for proving termination of programs. Well-known and very efficient techniques, like SAT algorithms and tools, have been recently proposed and used for implementing polynomial con...

This paper discusses the use of signed-digit representations in the implementation of fast and efficient residue-arithmetic units. Improvements to existing signed-digit modulo adders and multipliers are suggested and new converters for the residue signed-digit number system are described for the moduli . By extending an existing efficient signed-digit adder design to handle modulo operations, w...

We propose a method of using validated interval constraint contraction operators to build routines for numerical computation libraries. We illustrate the method by using it to construct a procedure that e ciently computes a small interval containing f 1(h) where f(x) = x sin(x). This can be transformed into a numerical routine by returning the midpoint of the interval and signalling an exceptio...

The RSA algorithm is the most widely used publickey cryptosystem today, but difficult to implement on embedded devices due to the computation-intense nature of its underlying arithmetic operations. Different techniques for efficient software implementation of the RSA algorithm have been proposed; these range from high-level approaches, such as exploiting the Chinese Remainder Theorem (CRT), dow...

Understanding an arithmetic operation implies, at minimum, knowing the direction of effects that the operation produces. However, many children and adults, even those who execute arithmetic procedures correctly, may lack this knowledge on some operations and types of numbers. To test this hypothesis, we presented pre-service teachers (Study 1), middle school students (Study 2), and math and sci...

In various telecommunication applications Digital Signal Processors are the key components in transferring the data between devices. The implementation of FIR filter on FPGA is based conventional methods increasing the need for considerable hardware resources, which in turn raises the circuit size and lowers the system speed. Most important operation performed in digital signal processing is Mu...

At CRYPTO 2016, Couteau, Peters and Pointcheval introduced a new primitive called encryption switching protocols, allowing to switch ciphertexts between two encryption schemes. If such an ESP is built with two schemes that are respectively additively and multiplicatively homomorphic, it naturally gives rise to a secure 2-party computation protocol. It is thus perfectly suited for evaluating fun...

Floating purpose is that the most vital a part of several fashionable chip. The amalgamate floating-point add–subtract unit is helpful for digital signal process (DSP) applications like quick Fourier rework (FFT) and separate circular function rework (DCT) butterfly operations. IEEE 754 normal specifies the ways for binary and decimal floating purpose arithmetic unit. Moreover, single precisene...

This paper is aimed at depicting the quality of functions of some of the aspects of attention in children with mild intellectual disabilities and their influence on the mastering of arithmetic operations, including addition and subtraction. The sample used in this study encompasses 60 pupils, both males and females. The criteria used in the selection of examinees included the IQ level of the st...