  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.
