In this paper we study complexity classes defined by path-restricted nondeterministic machines. We prove that for every language L in the class Few a polynomial time nondeterministic machine can be constructed which has f(x)+1 accepting paths for strings x ¿ L, and f(x) accepting paths for strings that are not in L, being f a function in PF. From this result we obtain lowness properties of the class Few, and positive relativizations of different counting classes.
CitationKöbler, J.; Schöning, U.; Torán, J. "Turing machines with few accepting computations". 1988.