Decoding complexity in wordreplacement translation models

Statistical machine translation is a relatively new approach to the longstanding problem of translating human languages by computer Current statistical techniques uncover trans lation rules from bilingual training texts and use those rules to translate new texts The general architecture is the sourcechannel model an English string is statistically gener ated source then statistically transformed into French channel In order to translate or decode a French string we look for the most likely English source We show that for the simplest form of statistical models this problem is NPcomplete ie probably exponential in the length of the observed sentence We trace this complexity to factors not present in other decoding problem