SYNTAX: A computer program to compress a sequence and to estimate its information content

Abstract

The determination of block-entropies is a well established method for the investigation of discrete data, also called symbols (7). There is a large variety of such symbolic sequences, ranging from texts written in natural languages, computer programs, neural spike trains, and biosequences. In this paper a new algorithm to construct a short context-free grammar (also called program or description) that generates a given sequence is introduced. It follows the general lines of a former algorithm, employed to compress biosequences (1,2) and to estimate the complexity of neural spike trains (4), which uses as valuation function the, so called, grammar complexity (2). The new algorithm employs the (observed) block-entropies instead. A variant, which employs a corrected "observed entropy", as discussed in (7) is also described. To illustrate its usefulness, applications of the program to the syntactic analysis of a sample biological sequences (DNA and RNA) is presented.