Under the auspices of the Computational Complexity Foundation (CCF)

REPORTS > KEYWORD > OBDD:
Reports tagged with OBDD:
TR97-019 | 5th May 1997
Martin Sauerhoff

#### A Lower Bound for Randomized Read-k-Times Branching Programs

In this paper, we are concerned with randomized OBDDs and randomized
read-k-times branching programs. We present an example of a Boolean
function which has polynomial size randomized OBDDs with small,
one-sided error, but only non-deterministic read-once branching
programs of exponential size. Furthermore, we discuss a lower bound
technique for randomized ... more >>>

TR97-021 | 16th May 1997
Farid Ablayev

#### Randomization and nondeterminsm are incomparable for ordered read-once branching programs

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 >>>

TR98-068 | 12th November 1998
Petr Savicky

#### On Random Orderings of Variables for Parity OBDDs

There are Boolean functions such that almost all orderings of
its variables yield an OBDD of polynomial size, but there are
also some exceptional orderings, for which the size is exponential.
We prove that for parity OBDDs the size for a random ordering
... more >>>

TR99-044 | 30th September 1999
Farid Ablayev

#### On Complexity of Regular $(1,+k)$-Branching Programs

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 >>>

TR01-020 | 20th February 2001
N. S. Narayanaswamy, C.E. Veni Madhavan

#### Lower Bounds for OBDDs and Nisan's pseudorandom generator

We present a new boolean function for which any Ordered Binary
Decision Diagram (OBDD) computing it has an exponential number
of nodes. This boolean function is obtained from Nisan's
pseudorandom generator to derandomize space bounded randomized
algorithms. Though the relation between hardness and randomness for
computational models is well ... more >>>

TR01-037 | 21st February 2001
Rustam Mubarakzjanov

#### Bounded-Width Probabilistic OBDDs and Read-Once Branching Programs are Incomparable

Restricted branching programs are considered by the investigation
of relationships between complexity classes of Boolean functions.
Read-once ordered branching programs (or OBDDs) form the most restricted class
of this computation model.
Since the problem of proving exponential lower bounds on the complexity
for general probabilistic OBDDs is open so ... more >>>

TR07-007 | 17th January 2007
Jan Krajicek

#### An exponential lower bound for a constraint propagation proof system based on ordered binary decision diagrams

We prove an exponential lower bound on the size of proofs
in the proof system operating with ordered binary decision diagrams
introduced by Atserias, Kolaitis and Vardi. In fact, the lower bound
applies to semantic derivations operating with sets defined by OBDDs.
We do not assume ... more >>>

TR08-059 | 20th May 2008
Farid Ablayev, Alexander Vasiliev

#### On the Computation of Boolean Functions by Quantum Branching Programs via Fingerprinting

Revisions: 1

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 >>>

TR10-030 | 18th February 2010
Airat Khasianov

#### Stronger Lower Bounds on Quantum OBDD for the Hidden Subgroup Problem

Revisions: 2

We consider the \emph{Hidden Subgroup} in the context of quantum \emph{Ordered Binary Decision Diagrams}.
We show several lower bounds for this function.
In this paper we also consider a slightly more general definition of the
hidden subgroup problem (in contrast to that in \cite{khashsp1}). It turns out that ... more >>>

TR15-048 | 14th February 2015

#### Width Hierarchy for $k$-OBDD of Small Width

Revisions: 1

In this paper was explored well known model $k$-OBDD. There are proven width based hierarchy of classes of boolean functions which computed by $k$-OBDD. The proof of hierarchy is based on sufficient condition of Boolean function's non representation as $k$-OBDD and complexity properties of Boolean
function SAF. This function is ... more >>>

TR17-176 | 15th November 2017

#### Exponential Separation between Quantum and Classical Ordered Binary Decision Diagrams, Reordering Method and Hierarchies

In this paper, we study quantum OBDD model, it is a restricted version of read-once quantum branching programs, with respect to "width" complexity. It is known that the maximal gap between deterministic and quantum complexities is exponential. But there are few examples of functions with such a gap. We present ... more >>>

TR17-179 | 20th November 2017
Alexander Knop

#### IPS-like Proof Systems Based on Binary Decision Diagrams

It is well-known that there is equivalence between ordered resolution and ordered binary decision diagrams (OBDD) [LNNW95]; i.e., for any unsatisfiable formula ?, the size of the smallest ordered resolution refutation of ? equal to the size of the smallest OBDD for the canonical search problem corresponding to ?. But ... more >>>

TR18-041 | 26th February 2018
Sam Buss, Dmitry Itsykson, Alexander Knop, Dmitry Sokolov

#### Reordering Rule Makes OBDD Proof Systems Stronger

Atserias, Kolaitis, and Vardi [AKV04] showed that the proof system of Ordered Binary Decision Diagrams with conjunction and weakening, OBDD($\land$, weakening), simulates CP* (Cutting Planes with unary coefficients). We show that OBDD($\land$, weakening) can give exponentially shorter proofs than dag-like cutting planes. This is proved by showing that the Clique-Coloring ... more >>>

TR19-001 | 5th January 2019
Dmitry Itsykson, Alexander Knop, Andrei Romashchenko, Dmitry Sokolov

#### On OBDD-based algorithms and proof systems that dynamically change order of variables

In 2004 Atserias, Kolaitis and Vardi proposed OBDD-based propositional proof systems that prove unsatisfiability of a CNF formula by deduction of identically false OBDD from OBDDs representing clauses of the initial formula. All OBDDs in such proofs have the same order of variables. We initiate the study of OBDD based ... more >>>

TR20-073 | 5th May 2020
Sam Buss, Dmitry Itsykson, Alexander Knop, Artur Riazanov, Dmitry Sokolov

#### Lower Bounds on OBDD Proofs with Several Orders

This paper is motivated by seeking lower bounds on OBDD($\land$, weakening, reordering) refutations, namely OBDD refutations that allow weakening and arbitrary reorderings. We first work with 1-NBP($\land$) refutations based on read-once nondeterministic branching programs. These generalize OBDD($\land$, reordering) refutations. There are polynomial size 1-NBP($\land$) refutations of the pigeonhole principle, hence ... more >>>

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