Improving calculations of the number of distinct alignments of two strings

The Number of Distinct Alignments of Two Strings

Alignment of Multiple Languages for Historical Comparison

An essential step in comparative reconstruction is to align corresponding phonological segments in the words being compared. To do this, one must search among huge numbers of potential alignments to find those that give a good phonetic fit. This is a hard computational problem, and it becomes exponentially more difficult when more than two strings are being aligned. In this paper I extend the g...

Tarski Number and Configuration Equations

The concept of configuration of groups which is defined in terms of finite partitions and finite strings of elements of the group is presented by Rosenblatt and Willis. To each set of configurations, a finite system of equations known as configuration equations, is associated. Rosenblatt and Willis proved that a discrete group G is amenable if and only if every possible instance of its configur...

Using both Binary and Residue Representations for Achieving Fast Converters in RNS

In this paper, a new method is introduced for improving the efficiency of the Residue Number System, which uses both binary and residue representations in order to represent a number. A residue number system uses the remainder of the division in several different modules. Conversion of a number to smaller ones and carrying out parallel calculations on these numbers greatly increase the speed of...

Using both Binary and Residue Representations for Achieving Fast Converters in RNS

In this paper, a new method is introduced for improving the efficiency of the Residue Number System, which uses both binary and residue representations in order to represent a number. A residue number system uses the remainder of the division in several different modules. Conversion of a number to smaller ones and carrying out parallel calculations on these numbers greatly increase the speed of...