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Finite state transducers, multitape automata and weighted automata have a lotin common. By studying their universal foundations, one can discover some newinsights into all of them. The main result presented here is the introductionof lexicographic finite state transducers, that could be seen as intermediatemodel between multitape automata and weighted transducers. Their mostsignificant advantage is being equivalent, but often exponentially smaller thaneven smallest nondeterministic automata without weights. Lexicographictransducers were discovered by taking inspiration from Eilenberg's algebraicapproach to automata and Solomonoff's treatment of a priori probability.Therefore, a quick and concise survey of those topics is presented, prior tointroducing lexicographic transducers.

Multitape automata and finite state transducers with lexicographic weights