51,215 research outputs found
SMT-Solvers in Action: Encoding and Solving Selected Problems in NP and EXPTIME
We compare the efficiency of seven modern SMT-solvers for several decision and combinatorial problems: the bounded Post correspondence problem (BPCP), the extended string correction problem (ESCP), and the Towers of Hanoi (ToH) of exponential solutions. For this purpose, we define new original reductions to SMT for all the above problems, and show their complexity. Our extensive experimental results allow for drawing quite interesting conclusions on efficiency and applicability of SMT-solvers depending on the theory used in the encoding
Adaptive Computation of the Swap-Insert Correction Distance
The Swap-Insert Correction distance from a string of length to
another string of length on the alphabet is the minimum
number of insertions, and swaps of pairs of adjacent symbols, converting
into . Contrarily to other correction distances, computing it is NP-Hard in
the size of the alphabet. We describe an algorithm computing this distance
in time within , where there are occurrences of
in , occurrences of in , and where
measures the
difficulty of the instance. The difficulty is bounded by above by various
terms, such as the length of the shortest string , and by the maximum number
of occurrences of a single character in . Those results illustrate how, in
many cases, the correction distance between two strings can be easier to
compute than in the worst case scenario.Comment: 16 pages, no figures, long version of the extended abstract accepted
to SPIRE 201
Level truncation and the quartic tachyon coupling
We discuss the convergence of level truncation in bosonic open string field
theory. As a test case we consider the calculation of the quartic tachyon
coupling . We determine the exact contribution from states up to
level L=28 and discuss the extrapolation by means of the BST
algorithm. We determine in a self-consistent way both the coupling and the
exponent of the leading correction to at finite that we
assume to be . The results are and
.}Comment: 17 pages, 2 eps figure
Pole Inflation - Shift Symmetry and Universal Corrections
An appealing explanation for the Planck data is provided by inflationary
models with a singular non-canonical kinetic term: a Laurent expansion of the
kinetic function translates into a potential with a nearly shift-symmetric
plateau in canonical fields. The shift symmetry can be broken at large field
values by including higher-order poles, which need to be hierarchically
suppressed in order not to spoil the inflationary plateau. The herefrom
resulting corrections to the inflationary dynamics and predictions are shown to
be universal at lowest order and possibly to induce power loss at large angular
scales. At lowest order there are no corrections from a pole of just one order
higher and we argue that this phenomenon is related to the well-known extended
no-scale structure arising in string theory scenarios. Finally, we outline
which other corrections may arise from string loop effects.Comment: twocolumn, 9 pages, 1 figure; v2: clarifications and refs added, JHEP
layout, 19 page
A practical index for approximate dictionary matching with few mismatches
Approximate dictionary matching is a classic string matching problem
(checking if a query string occurs in a collection of strings) with
applications in, e.g., spellchecking, online catalogs, geolocation, and web
searchers. We present a surprisingly simple solution called a split index,
which is based on the Dirichlet principle, for matching a keyword with few
mismatches, and experimentally show that it offers competitive space-time
tradeoffs. Our implementation in the C++ language is focused mostly on data
compaction, which is beneficial for the search speed (e.g., by being cache
friendly). We compare our solution with other algorithms and we show that it
performs better for the Hamming distance. Query times in the order of 1
microsecond were reported for one mismatch for the dictionary size of a few
megabytes on a medium-end PC. We also demonstrate that a basic compression
technique consisting in -gram substitution can significantly reduce the
index size (up to 50% of the input text size for the DNA), while still keeping
the query time relatively low
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