Index Generation Functions Research Articles

Heuristic Minimization of Symmetric Index Generation Functions utilizing their Properties

This paper focuses on the minimization of index generation functions, which are useful in telecommunication and cybersecurity. In particular, we target a specific class of those functions, i.e., symmetric index generation functions. The application of logic synthesis methods to such functions can often lead to a representation that uses fewer variables. We analyze the properties of those functions and how they can be used to minimize the number of variables.

Index Generation Functions

This chapter introduces index generation functions with various applications. Then, it shows a method to realize index generation functions by LUTs.

Optimization on the Complementation Procedure Towards Efficient Implementation of the Index Generation Function

Abstract In the era of big data, solutions are desired that would be capable of efficient data reduction. This paper presents a summary of research on an algorithm for complementation of a Boolean function which is fundamental for logic synthesis and data mining. Successively, the existing problems and their proposed solutions are examined, including the analysis of current implementations of the algorithm. Then, methods to speed up the computation process and efficient parallel implementation of the algorithm are shown; they include optimization of data representation, recursive decomposition, merging, and removal of redundant data. Besides the discussion of computational complexity, the paper compares the processing times of the proposed solution with those for the well-known analysis and data mining systems. Although the presented idea is focused on searching for all possible solutions, it can be restricted to finding just those of the smallest size. Both approaches are of great application potential, including proving mathematical theorems, logic synthesis, especially index generation functions, or data processing and mining such as feature selection, data discretization, rule generation, etc. The problem considered is NP-hard, and it is easy to point to examples that are not solvable within the expected amount of time. However, the solution allows the barrier of computations to be moved one step further. For example, the unique algorithm can calculate, as the only one at the moment, all minimal sets of features for few standard benchmarks. Unlike many existing methods, the algorithm additionally works with undetermined values. The result of this research is an easily extendable experimental software that is the fastest among the tested solutions and the data mining systems.

A Balanced Decision Tree Based Heuristic for Linear Decomposition of Index Generation Functions

A Balanced Decision Tree Based Heuristic for Linear Decomposition of Index Generation Functions

Synthesis Algorithm for Parallel Index Generator

The index generation function is a multi-valued logic function which checks if the given input vector is a registered or not, and returns its index value if the vector is registered. If the latency of the operation is critical, dedicated hardware is used for implementing the index generation functions. This paper proposes a method implementing the index generation functions using parallel index generator. A novel and efficient algorithm called ‘conflict free partitioning’ is proposed to synthesize parallel index generators. Experimental results show the proposed method outperforms other existing methods. Also, A novel architecture of index generator which is suitable for parallelized implementation is introduced. A new architecture has advantages in the sense of both area and delay.

A Method to Find Linear Decompositions for Incompletely Specified Index Generation Functions Using Difference Matrix

A Method to Find Linear Decompositions for Incompletely Specified Index Generation Functions Using Difference Matrix