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Undecidability in integer weighted finite automata

Halava V., Harju T.

Fundamenta Informaticae

1999

Vol. 38, Nr 1,2

189-200

It is shown that the universe problem L(Ag) = A* is undecidable for 4-state finite automata A with integer weight function g on its transitions. This holds even in the case, where A is acyclic and the weighting g satisfies the unimodality condition. The language L(Ag) is defined as the set of words w for which there exists a path p of A having zero weight, that is, g(p) = 0.