This paper introduces and investigates decision problems for numberless probabilistic automata, i.e. probabilistic automata where the support of each probabilistic transitions is specified, but the exact values of the probabilities are not. A numberless probabilistic automaton can be instantiated into a probabilistic automaton by specifying the exact values of the non-zero probabilistic transit...

Let ďc be computable reducibility on ceers. We show that for every computably enumerable equivalence relation (or ceer) R with infinitely many equivalence classes, the index sets ti : Ri ďc Ru (with R non-universal), ti : Ri ěc Ru, and ti : Ri ”c Ru are Σ3 complete, whereas in case R has only finitely many equivalence classes, we have that ti : Ri ďc Ru is Π2 complete, and ti : Ri ěc Ru (with R...

We prove that every disjoint NP-pair is polynomial-time, many-one equivalent to the canonical disjoint NP-pair of some propositional proof system. Therefore, the degree structure of the class of disjoint NP-pairs and of all canonical pairs is identical. Secondly, we show that this degree structure is not superficial: Assuming there exist P-inseparable disjoint pairs, there exist intermediate di...