110 research outputs found
Tree Compression with Top Trees Revisited
We revisit tree compression with top trees (Bille et al, ICALP'13) and
present several improvements to the compressor and its analysis. By
significantly reducing the amount of information stored and guiding the
compression step using a RePair-inspired heuristic, we obtain a fast compressor
achieving good compression ratios, addressing an open problem posed by Bille et
al. We show how, with relatively small overhead, the compressed file can be
converted into an in-memory representation that supports basic navigation
operations in worst-case logarithmic time without decompression. We also show a
much improved worst-case bound on the size of the output of top-tree
compression (answering an open question posed in a talk on this algorithm by
Weimann in 2012).Comment: SEA 201
Evaluating Matrix Circuits
The circuit evaluation problem (also known as the compressed word problem)
for finitely generated linear groups is studied. The best upper bound for this
problem is , which is shown by a reduction to polynomial
identity testing. Conversely, the compressed word problem for the linear group
is equivalent to polynomial identity testing. In
the paper, it is shown that the compressed word problem for every finitely
generated nilpotent group is in . Within
the larger class of polycyclic groups we find examples where the compressed
word problem is at least as hard as polynomial identity testing for skew
arithmetic circuits
Unary Pushdown Automata and Straight-Line Programs
We consider decision problems for deterministic pushdown automata over a
unary alphabet (udpda, for short). Udpda are a simple computation model that
accept exactly the unary regular languages, but can be exponentially more
succinct than finite-state automata. We complete the complexity landscape for
udpda by showing that emptiness (and thus universality) is P-hard, equivalence
and compressed membership problems are P-complete, and inclusion is
coNP-complete. Our upper bounds are based on a translation theorem between
udpda and straight-line programs over the binary alphabet (SLPs). We show that
the characteristic sequence of any udpda can be represented as a pair of
SLPs---one for the prefix, one for the lasso---that have size linear in the
size of the udpda and can be computed in polynomial time. Hence, decision
problems on udpda are reduced to decision problems on SLPs. Conversely, any SLP
can be converted in logarithmic space into a udpda, and this forms the basis
for our lower bound proofs. We show coNP-hardness of the ordered matching
problem for SLPs, from which we derive coNP-hardness for inclusion. In
addition, we complete the complexity landscape for unary nondeterministic
pushdown automata by showing that the universality problem is -hard, using a new class of integer expressions. Our techniques have
applications beyond udpda. We show that our results imply -completeness for a natural fragment of Presburger arithmetic and coNP lower
bounds for compressed matching problems with one-character wildcards
Compressed Membership for NFA (DFA) with Compressed Labels is in NP (P)
In this paper, a compressed membership problem for finite automata, both
deterministic and non-deterministic, with compressed transition labels is
studied. The compression is represented by straight-line programs (SLPs), i.e.
context-free grammars generating exactly one string. A novel technique of
dealing with SLPs is introduced: the SLPs are recompressed, so that substrings
of the input text are encoded in SLPs labelling the transitions of the NFA
(DFA) in the same way, as in the SLP representing the input text. To this end,
the SLPs are locally decompressed and then recompressed in a uniform way.
Furthermore, such recompression induces only small changes in the automaton, in
particular, the size of the automaton remains polynomial.
Using this technique it is shown that the compressed membership for NFA with
compressed labels is in NP, thus confirming the conjecture of Plandowski and
Rytter and extending the partial result of Lohrey and Mathissen; as it is
already known, that this problem is NP-hard, we settle its exact computational
complexity. Moreover, the same technique applied to the compressed membership
for DFA with compressed labels yields that this problem is in P; for this
problem, only trivial upper-bound PSPACE was known
Deciding Equivalence of Linear Tree-to-Word Transducers in Polynomial Time
We show that the equivalence of deterministic linear top-down tree-to-word
transducers is decidable in polynomial time. Linear tree-to-word transducers
are non-copying but not necessarily order-preserving and can be used to express
XML and other document transformations. The result is based on a partial normal
form that provides a basic characterization of the languages produced by linear
tree-to-word transducers.Comment: short version of this paper will be published in the proceedings of
the 20th Conference on Developments in Language Theory (DLT 2016), Montreal,
Canad
Processing Succinct Matrices and Vectors
We study the complexity of algorithmic problems for matrices that are
represented by multi-terminal decision diagrams (MTDD). These are a variant of
ordered decision diagrams, where the terminal nodes are labeled with arbitrary
elements of a semiring (instead of 0 and 1). A simple example shows that the
product of two MTDD-represented matrices cannot be represented by an MTDD of
polynomial size. To overcome this deficiency, we extended MTDDs to MTDD_+ by
allowing componentwise symbolic addition of variables (of the same dimension)
in rules. It is shown that accessing an entry, equality checking, matrix
multiplication, and other basic matrix operations can be solved in polynomial
time for MTDD_+-represented matrices. On the other hand, testing whether the
determinant of a MTDD-represented matrix vanishes PSPACE$-complete, and the
same problem is NP-complete for MTDD_+-represented diagonal matrices. Computing
a specific entry in a product of MTDD-represented matrices is #P-complete.Comment: An extended abstract of this paper will appear in the Proceedings of
CSR 201
Managing Compressed Structured Text
[Definition]: Compressing structured text is the problem of creating a reduced-space representation from which the original
data can be re-created exactly. Compared to plain text compression, the goal is to take advantage of the structural
properties of the data. A more ambitious goal is that of being able of manipulating this text in compressed form,
without decompressing it. This entry focuses on compressing, navigating, and searching structured text, as those
are the areas where more advances have been made
Silent Transitions in Automata with Storage
We consider the computational power of silent transitions in one-way automata
with storage. Specifically, we ask which storage mechanisms admit a
transformation of a given automaton into one that accepts the same language and
reads at least one input symbol in each step.
We study this question using the model of valence automata. Here, a finite
automaton is equipped with a storage mechanism that is given by a monoid.
This work presents generalizations of known results on silent transitions.
For two classes of monoids, it provides characterizations of those monoids that
allow the removal of \lambda-transitions. Both classes are defined by graph
products of copies of the bicyclic monoid and the group of integers. The first
class contains pushdown storages as well as the blind counters while the second
class contains the blind and the partially blind counters.Comment: 32 pages, submitte
Dislocation-mediated plasticity in the AlCu {\theta}-phase
The deformation behaviour of the intermetallic AlCu-phase was
investigated using atomistic simulations and micropillar compression, where
slip on the unexpected {211} and {022} slip planes was revealed. Additionally,
all possible slip systems for the intermetallic phases were further evaluated
and a preference for the activation of slip systems based on their effective
interplanar distances as well as the effective Burgers vector is proposed. The
effective interplanar distance corresponds to the manually determined
interplanar distance, whereas the effective Burgers vector takes a potential
dislocation dissociation into account. This new order is: {211}1/2,
{022}1/2 and {022}, {110}, {310}, {022},
{110}1/2, {112} and {112}1/2 from high to low ratio of
deff/beff. Also, data on the critical resolved shear stresses of several of
these slip systems were measured.Comment: 27 pages, 17 figure
Human T-cell leukemia virus type I infection of monocytes and microglial cells in primary human cultures.
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