# Finite inductive sequence: Factoring technique

## Abstract

This thesis considers finite sequences of symbols extracted from an alphabet set. In this case, the alphabet set is the positive integers. The underlying hypotheses is that such finite sequence is finitely inductive (FI). Finitely inductive implies that a symbol at any position can be determined by the symbols preceding it. The technique used is called FI - Factoring. FI is primarily used to learn about the presence of relationships between symbols of arbitrary sequences. Note that indicating the presence of a relationship does not necessarily provide information about the nature of that relationship. To gain that knowledge further analysis is required.

Consequently, the pattern recognition technique involves factoring a sequence of data into a series of small sequences called implicants. The collection of implicants is then form a ruling. This ruling is used to match other sequences, and sequences of residual. FI factoring technique focuses on direct analysis of the structure of individual sequences.

Beginning with a given finite sequence of symbols, the factoring algorithm will describe the underlying structure of each sequence. Each input sequence which in this case is finite, is characterized by function tables or ruling describing the structure of each sequence.