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 ... more >>>

We develop quantum fingerprinting technique for constructing quantum
branching programs (QBPs), which are considered as circuits with an
ability to use classical bits as control variables.

We demonstrate our approach constructing optimal quantum ordered
binary decision diagram (QOBDD) for $MOD_m$ and $DMULT_n$ Boolean
functions. The construction of our technique also ... more >>>

We prove upper and lower bounds on the power of quantum and stochastic
branching programs of bounded width. We show any NC^1 language can
be accepted exactly by a width-2 quantum branching program of
polynomial length, in contrast to the classical case where width 5 is
necessary unless \NC^1=\ACC. ... more >>>

A regular $(1,+k)$-branching program ($(1,+k)$-ReBP) is an
ordinary branching program with the following restrictions: (i)
along every consistent path at most $k$ variables are tested more
than once, (ii) for each node $v$ on all paths from the source to
$v$ the same set $X(v)\subseteq X$ of variables is ... more >>>

The superposition (or composition) problem is a problem of
representation of a function $f$ by a superposition of "simpler" (in a
different meanings) set $\Omega$ of functions. In terms of circuits
theory this means a possibility of computing $f$ by a finite circuit
with 1 fan-out gates $\Omega$ of functions. ... more >>>

We prove an exponential lower bound ($2^{\Omega(n/\log n)}$) on the
size of any randomized ordered read-once branching program
computing integer multiplication. Our proof depends on proving
a new lower bound on Yao's randomized one-way communication
complexity of certain boolean functions. It generalizes to some
other ... more >>>

We introduce a model of a {\em randomized branching program}
in a natural way similar to the definition of a randomized circuit.
We exhibit an explicit boolean function
$f_{n}:\{0,1\}^{n}\to\{0,1\}$ for which we prove that:

1) $f_{n}$ can be computed by a polynomial size randomized
... more >>>

In the manuscript F. Ablayev and M. Karpinski, On the power of
randomized branching programs (generalization of ICALP'96 paper
results for the case of pure boolean function, available at
http://www.ksu.ru/~ablayev) we exhibited a simple boolean functions
$f_n$ in $n$ variables such that:

1) $f_{n}$ can be computed ... more >>>

We define the notion of a randomized branching program in
the natural way similar to the definition of a randomized
circuit. We exhibit an explicit function $f_{n}$ for which
we prove that:
1) $f_{n}$ can be computed by polynomial size randomized
... more >>>