1,165 research outputs found
Optimised determinisation and completion of finite tree automata
Determinisation and completion of finite tree automata are important
operations with applications in program analysis and verification. However, the
complexity of the classical procedures for determinisation and completion is
high. They are not practical procedures for manipulating tree automata beyond
very small ones. In this paper we develop an algorithm for determinisation and
completion of finite tree automata, whose worst-case complexity remains
unchanged, but which performs far better than existing algorithms in practice.
The critical aspect of the algorithm is that the transitions of the
determinised (and possibly completed) automaton are generated in a potentially
very compact form called product form, which can reduce the size of the
representation dramatically. Furthermore, the representation can often be used
directly when manipulating the determinised automaton. The paper contains an
experimental evaluation of the algorithm on a large set of tree automata
examples
Construction of Near-Optimum Burst Erasure Correcting Low-Density Parity-Check Codes
In this paper, a simple, general-purpose and effective tool for the design of
low-density parity-check (LDPC) codes for iterative correction of bursts of
erasures is presented. The design method consists in starting from the
parity-check matrix of an LDPC code and developing an optimized parity-check
matrix, with the same performance on the memory-less erasure channel, and
suitable also for the iterative correction of single bursts of erasures. The
parity-check matrix optimization is performed by an algorithm called pivot
searching and swapping (PSS) algorithm, which executes permutations of
carefully chosen columns of the parity-check matrix, after a local analysis of
particular variable nodes called stopping set pivots. This algorithm can be in
principle applied to any LDPC code. If the input parity-check matrix is
designed for achieving good performance on the memory-less erasure channel,
then the code obtained after the application of the PSS algorithm provides good
joint correction of independent erasures and single erasure bursts. Numerical
results are provided in order to show the effectiveness of the PSS algorithm
when applied to different categories of LDPC codes.Comment: 15 pages, 4 figures. IEEE Trans. on Communications, accepted
(submitted in Feb. 2007
Necessity of Superposition of Macroscopically Distinct States for Quantum Computational Speedup
For quantum computation, we investigate the conjecture that the superposition
of macroscopically distinct states is necessary for a large quantum speedup.
Although this conjecture was supported for a circuit-based quantum computer
performing Shor's factoring algorithm [A. Ukena and A. Shimizu, Phys. Rev. A69
(2004) 022301], it needs to be generalized for it to be applicable to a large
class of algorithms and/or other models such as measurement-based quantum
computers. To treat such general cases, we first generalize the indices for the
superposition of macroscopically distinct states. We then generalize the
conjecture, using the generalized indices, in such a way that it is
unambiguously applicable to general models if a quantum algorithm achieves
exponential speedup. On the basis of this generalized conjecture, we further
extend the conjecture to Grover's quantum search algorithm, whose speedup is
large but quadratic. It is shown that this extended conjecture is also correct.
Since Grover's algorithm is a representative algorithm for unstructured
problems, the present result further supports the conjecture.Comment: 18 pages, 5 figures. Fixed typos throughout the manuscript. This
version has been publishe
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