Statistical analysis of the Indus script using $n$-grams

Abstract: The Indus script is one of the major undeciphered scripts of the ancient world. The small size of the corpus, the absence of bilingual texts, and the lack of definite knowledge of the underlying language has frustrated efforts at decipherment since the discovery of the remains of the Indus civilisation. Recently, some researchers have questioned the premise that the Indus script encodes spoken language. Building on previous statistical approaches, we apply the tools of statistical language processing, specifically $n$-gram Markov chains, to analyse the Indus script for syntax. Our main results are that the script has well-defined signs which begin and end texts, that there is directionality and strong correlations in the sign order, and that there are groups of signs which appear to have identical syntactic function. All these require no {\it a priori} suppositions regarding the syntactic or semantic content of the signs, but follow directly from the statistical analysis. Using information theoretic measures, we find the information in the script to be intermediate between that of a completely random and a completely fixed ordering of signs. Our study reveals that the Indus script is a structured sign system showing features of a formal language, but, at present, cannot conclusively establish that it encodes {\it natural} language. Our $n$-gram Markov model is useful for predicting signs which are missing or illegible in a corpus of Indus texts. This work forms the basis for the development of a stochastic grammar which can be used to explore the syntax of the Indus script in greater detail.