6,965 research outputs found
The Rightmost Equal-Cost Position Problem
LZ77-based compression schemes compress the input text by replacing factors
in the text with an encoded reference to a previous occurrence formed by the
couple (length, offset). For a given factor, the smallest is the offset, the
smallest is the resulting compression ratio. This is optimally achieved by
using the rightmost occurrence of a factor in the previous text. Given a cost
function, for instance the minimum number of bits used to represent an integer,
we define the Rightmost Equal-Cost Position (REP) problem as the problem of
finding one of the occurrences of a factor which cost is equal to the cost of
the rightmost one. We present the Multi-Layer Suffix Tree data structure that,
for a text of length n, at any time i, it provides REP(LPF) in constant time,
where LPF is the longest previous factor, i.e. the greedy phrase, a reference
to the list of REP({set of prefixes of LPF}) in constant time and REP(p) in
time O(|p| log log n) for any given pattern p
On-line construction of position heaps
We propose a simple linear-time on-line algorithm for constructing a position
heap for a string [Ehrenfeucht et al, 2011]. Our definition of position heap
differs slightly from the one proposed in [Ehrenfeucht et al, 2011] in that it
considers the suffixes ordered from left to right. Our construction is based on
classic suffix pointers and resembles the Ukkonen's algorithm for suffix trees
[Ukkonen, 1995]. Using suffix pointers, the position heap can be extended into
the augmented position heap that allows for a linear-time string matching
algorithm [Ehrenfeucht et al, 2011].Comment: to appear in Journal of Discrete Algorithm
Computing LZ77 in Run-Compressed Space
In this paper, we show that the LZ77 factorization of a text T {\in\Sigma^n}
can be computed in O(R log n) bits of working space and O(n log R) time, R
being the number of runs in the Burrows-Wheeler transform of T reversed. For
extremely repetitive inputs, the working space can be as low as O(log n) bits:
exponentially smaller than the text itself. As a direct consequence of our
result, we show that a class of repetition-aware self-indexes based on a
combination of run-length encoded BWT and LZ77 can be built in asymptotically
optimal O(R + z) words of working space, z being the size of the LZ77 parsing
Separation of Test-Free Propositional Dynamic Logics over Context-Free Languages
For a class L of languages let PDL[L] be an extension of Propositional
Dynamic Logic which allows programs to be in a language of L rather than just
to be regular. If L contains a non-regular language, PDL[L] can express
non-regular properties, in contrast to pure PDL.
For regular, visibly pushdown and deterministic context-free languages, the
separation of the respective PDLs can be proven by automata-theoretic
techniques. However, these techniques introduce non-determinism on the automata
side. As non-determinism is also the difference between DCFL and CFL, these
techniques seem to be inappropriate to separate PDL[DCFL] from PDL[CFL].
Nevertheless, this separation is shown but for programs without test operators.Comment: In Proceedings GandALF 2011, arXiv:1106.081
RDF Querying
Reactive Web systems, Web services, and Web-based publish/
subscribe systems communicate events as XML messages, and in
many cases require composite event detection: it is not sufficient to react
to single event messages, but events have to be considered in relation to
other events that are received over time.
Emphasizing language design and formal semantics, we describe the
rule-based query language XChangeEQ for detecting composite events.
XChangeEQ is designed to completely cover and integrate the four complementary
querying dimensions: event data, event composition, temporal
relationships, and event accumulation. Semantics are provided as
model and fixpoint theories; while this is an established approach for rule
languages, it has not been applied for event queries before
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