Arithmetics-Based Decomposition of Numeral Words -- Arithmetic
  Conditions give the Unpacking Strategy
Isidor Konrad Maier Matthias Wolff
In this paper we present a novel numeral decomposer that is designed to
revert Hurford's Packing Strategy. The Packing Strategy is a model on how
numeral words are formed out of smaller numeral words by recursion. The
decomposer does not simply check decimal digits but it also works for numerals
formed on base 20 or any other base or even combinations of different bases.
All assumptions that we use are justified with Hurford's Packing Strategy. The
decomposer reads through the numeral. When it finds a sub-numeral, it checks
arithmetic conditions to decide whether or not to unpack the sub-numeral. The
goal is to unpack those numerals that can sensibly be substituted by similar
numerals. E.g., in 'twenty-seven thousand and two hundred and six' it should
unpack 'twenty-seven' and 'two hundred and six', as those could each be
sensibly replaced by any numeral from 1 to 999. Our most used condition is: If
S is a substitutable sub-numeral of a numeral N, then 2*value(S) < value(N). We
have tested the decomposer on numeral systems in 254 different natural
languages. We also developed a reinforcement learning algorithm based on the
decomposer. Both algorithms' code and the results are open source on GitHub.