710 research outputs found
Quantum Certificate Complexity
Given a Boolean function f, we study two natural generalizations of the
certificate complexity C(f): the randomized certificate complexity RC(f) and
the quantum certificate complexity QC(f). Using Ambainis' adversary method, we
exactly characterize QC(f) as the square root of RC(f). We then use this result
to prove the new relation R0(f) = O(Q2(f)^2 Q0(f) log n) for total f, where R0,
Q2, and Q0 are zero-error randomized, bounded-error quantum, and zero-error
quantum query complexities respectively. Finally we give asymptotic gaps
between the measures, including a total f for which C(f) is superquadratic in
QC(f), and a symmetric partial f for which QC(f) = O(1) yet Q2(f) = Omega(n/log
n).Comment: 9 page
Deterministic Computations on a PRAM with Static Processor and Memory Faults.
We consider Parallel Random Access Machine (PRAM) which has some processors
and memory cells faulty. The faults considered are static, i.e., once the
machine starts to operate, the operational/faulty status of PRAM components
does not change. We develop a deterministic simulation of a fully operational
PRAM on a similar faulty machine which has constant fractions of faults among
processors and memory cells. The simulating PRAM has processors and
memory cells, and simulates a PRAM with processors and a constant fraction
of memory cells. The simulation is in two phases: it starts with
preprocessing, which is followed by the simulation proper performed in a
step-by-step fashion. Preprocessing is performed in time . The slowdown of a step-by-step part of the simulation is
On the parity complexity measures of Boolean functions
The parity decision tree model extends the decision tree model by allowing
the computation of a parity function in one step. We prove that the
deterministic parity decision tree complexity of any Boolean function is
polynomially related to the non-deterministic complexity of the function or its
complement. We also show that they are polynomially related to an analogue of
the block sensitivity. We further study parity decision trees in their
relations with an intermediate variant of the decision trees, as well as with
communication complexity.Comment: submitted to TCS on 16-MAR-200
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