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Electronic Colloquium on Computational Complexity

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All reports by Author Philipp Woelfel:

TR04-107 | 24th November 2004
Ingo Wegener, Philipp Woelfel

New Results on the Complexity of the Middle Bit of Multiplication

Revisions: 1

It is well known that the hardest bit of integer multiplication is the middle bit, i.e. MUL_{n-1,n}.
This paper contains several new results on its complexity.
First, the size s of randomized read-k branching programs, or, equivalently, its space (log s) is investigated.
A randomized algorithm for MUL_{n-1,n} with k=O(log ... more >>>

TR01-101 | 14th December 2001
Philipp Woelfel

A Lower Bound Technique for Restricted Branching Programs and Applications

We present a new lower bound technique for two types of restricted
Branching Programs (BPs), namely for read-once BPs (BP1s) with
restricted amount of nondeterminism and for (1,+k)-BPs. For this
technique, we introduce the notion of (strictly) k-wise l-mixed
Boolean functions, which generalizes the concept of l-mixedness ... more >>>

TR01-073 | 24th October 2001
Beate Bollig, Philipp Woelfel, Stephan Waack

Parity Graph-driven Read-Once Branching Programs and an Exponential Lower Bound for Integer Multiplication

Revisions: 1

Branching programs are a well-established computation model
for Boolean functions, especially read-once branching programs
have been studied intensively. Exponential lower bounds for
deterministic and nondeterministic read-once branching programs
are known for a long time. On the other hand, the problem of
proving superpolynomial lower bounds ... more >>>

TR00-046 | 19th June 2000
Philipp Woelfel

New Bounds on the OBDD-Size of Integer Multiplication via Universal Hashing

Ordered binary decision diagrams (OBDDs) belong to the most important
representation types for Boolean functions. Although they allow
important operations such as satisfiability test and equality test to
be performed efficiently, their limitation lies in the fact, that they
may require exponential size for important functions. Bryant ... more >>>

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