We consider the Hidden Subgroup, and Equality-related problems
in the context of quantum Ordered Binary Decision Diagrams. For the
decision versions of considered problems we show polynomial upper bounds in
terms of quantum OBDD width. We apply a new modification of the fingerprinting
technique and present the algorithms in circuit notation. Our algorithms
require at most logarithmic number of qubits.

1. Generalized Equality section removed;
2. Permutation Matrix Test section added to the paper;
3. HSP section extended with extra details;
4. Minor typos corrected.

We consider Generalized Equality, the Hidden Subgroup,
and related problems in the context of quantum Ordered Binary
Decision Diagrams. For the decision versions of considered problems
we show polynomial upper bounds in terms of quantum OBDD width. We
apply a new modification of the fingerprinting technique and present
the algorithms in circuit notation. Our algorithms require at most
logarithmic number of qubits.