On number systems with negative digits

We study a"rbitra.ry number systems which allow negative digits. We show that the set of nonnegative integers represented by a number system -lf = (n,rn1,. . . ,mo) is n-recognizable. Using the theory of [-recognizable sets, we prove that the equivalence problem for number systems is decidable. We show that the degree of ambiguity of a given number system can be eflectively