Related papers: Stack and register complexity of radix conversions
In this paper, the optimality of ternary arithmetic is investigated under strict mathematical formulation. The arithmetic systems are presented in generic form, as the means to encode numeric values, and the choice of radix is asserted as…
The goal of rigid registration is to align a source surface $ X $ to a target surface $ Y $. The alignment process involves iteratively transforming $ X $ closer and closer to $ Y $, such that $ X=Z^0 \rightarrow Z^1 \rightarrow Z^2…
Presented here are algorithms for converting between (decimal) scientific-notation and (binary) IEEE-754 double-precision floating-point numbers. By employing a rounding integer quotient operation these algorithms are much simpler than…
We study the configuration space of rectangulations and convex subdivisions of $n$ points in the plane. It is shown that a sequence of $O(n\log n)$ elementary flip and rotate operations can transform any rectangulation to any other…
We present algorithms for the type-IV discrete cosine transform (DCT-IV) and discrete sine transform (DST-IV), as well as for the modified discrete cosine transform (MDCT) and its inverse, that achieve a lower count of real multiplications…
We study sorting machines consisting of a stack and a pop stack in series, with or without a queue between them. While there are, a priori, four such machines, only two are essentially different: a pop stack followed directly by a stack,…
In this paper, we present a partial survey of the tools borrowed from tensor algebra, which have been utilized recently in Statistics and Signal Processing. It is shown why the decompositions well known in linear algebra can hardly be…
Learning rich and compact representations is an open topic in many fields such as object recognition or image retrieval. Deep neural networks have made a major breakthrough during the last few years for these tasks but their representations…
Generalizing work of K\"unnemann, Paturi, and Schneider [ICALP 2017], we study a wide class of high-dimensional dynamic programming (DP) problems in which one must find the shortest path between two points in a high-dimensional grid given a…
This paper compares the performance of conventional radix-2 program counters with program counters based on Feedback Shift Registers (FSRs), a class of cyclic sequence generator. FSR counters have constant time scaling with bit-width, $N$,…
We consider the problem of upper bounding the number of circular transpositions needed to sort a permutation. It is well known that any permutation can be sorted using at most $n(n-1)/2$ adjacent transpositions. We show that, if we allow…
Arithmetic complexity is considered simpler to understand than Boolean complexity, namely computing Boolean functions via logical gates. And indeed, we seem to have significantly more lower bound techniques and results in arithmetic…
The paper studies the main aspects of the realization of 2 x 2 ternary reversible circuits based on cycles, considering the results of the realization of all 362,880 2 x 2 ternary reversible functions. It has been shown that in most cases,…
The challenge of mastering computational tasks of enormous size tends to frequently override questioning the quality of the numerical outcome in terms of accuracy. By this we do not mean the accuracy within the discrete setting, which…
Learning to Rank has traditionally considered settings where given the relevance information of objects, the desired order in which to rank the objects is clear. However, with today's large variety of users and layouts this is not always…
We extend the circuit model of quantum computation so that the wiring between gates is soft-coded within registers inside the gates. The addresses in these registers can be manipulated and put into superpositions. This aims at capturing…
When sharing or logging numerical data, we must convert binary floating-point numbers into their decimal string representations. For example, the number $\pi$ might become 3.1415927. Engineers have perfected many algorithms for producing…
Computational problems are classified into computable and uncomputable problems. If there exists an effective procedure (algorithm) to compute a problem then the problem is computable otherwise it is uncomputable. Turing machines can…
This work studies rearrangement problems involving the sorting of robots or objects in stack-like containers, which can be accessed only from one side. Two scenarios are considered: one where every robot or object needs to reach a…
Finding the product of two polynomials is an essential and basic problem in computer algebra. While most previous results have focused on the worst-case complexity, we instead employ the technique of adaptive analysis to give an improvement…