1,096 research outputs found
Reachability in Higher-Order-Counters
Higher-order counter automata (\HOCS) can be either seen as a restriction of
higher-order pushdown automata (\HOPS) to a unary stack alphabet, or as an
extension of counter automata to higher levels. We distinguish two principal
kinds of \HOCS: those that can test whether the topmost counter value is zero
and those which cannot.
We show that control-state reachability for level \HOCS with -test is
complete for \mbox{}-fold exponential space; leaving out the -test
leads to completeness for \mbox{}-fold exponential time. Restricting
\HOCS (without -test) to level , we prove that global (forward or
backward) reachability analysis is \PTIME-complete. This enhances the known
result for pushdown systems which are subsumed by level \HOCS without
-test.
We transfer our results to the formal language setting. Assuming that \PTIME
\subsetneq \PSPACE \subsetneq \mathbf{EXPTIME}, we apply proof ideas of
Engelfriet and conclude that the hierarchies of languages of \HOPS and of \HOCS
form strictly interleaving hierarchies. Interestingly, Engelfriet's
constructions also allow to conclude immediately that the hierarchy of
collapsible pushdown languages is strict level-by-level due to the existing
complexity results for reachability on collapsible pushdown graphs. This
answers an open question independently asked by Parys and by Kobayashi.Comment: Version with Full Proofs of a paper that appears at MFCS 201
Macro-evolutionary models and coalescent point processes: The shape and probability of reconstructed phylogenies
Forward-time models of diversification (i.e., speciation and extinction)
produce phylogenetic trees that grow "vertically" as time goes by. Pruning the
extinct lineages out of such trees leads to natural models for reconstructed
trees (i.e., phylogenies of extant species). Alternatively, reconstructed trees
can be modelled by coalescent point processes (CPP), where trees grow
"horizontally" by the sequential addition of vertical edges. Each new edge
starts at some random speciation time and ends at the present time; speciation
times are drawn from the same distribution independently. CPP lead to extremely
fast computation of tree likelihoods and simulation of reconstructed trees.
Their topology always follows the uniform distribution on ranked tree shapes
(URT). We characterize which forward-time models lead to URT reconstructed
trees and among these, which lead to CPP reconstructed trees. We show that for
any "asymmetric" diversification model in which speciation rates only depend on
time and extinction rates only depend on time and on a non-heritable trait
(e.g., age), the reconstructed tree is CPP, even if extant species are
incompletely sampled. If rates additionally depend on the number of species,
the reconstructed tree is (only) URT (but not CPP). We characterize the common
distribution of speciation times in the CPP description, and discuss incomplete
species sampling as well as three special model cases in detail: 1) extinction
rate does not depend on a trait; 2) rates do not depend on time; 3) mass
extinctions may happen additionally at certain points in the past
Deciding determinism of caterpillar expressions
AbstractCaterpillar expressions have been introduced by Brüggemann-Klein and Wood for applications in markup languages. Caterpillar expressions provide a convenient formalism for specifying the operation of tree-walking automata on unranked trees. Here we give a formal definition of determinism of caterpillar expressions that is based on the language of instruction sequences defined by the expression. We show that determinism of caterpillar expressions can be decided in polynomial time
Spare Parts And Maintenance Optimization In A Mobile Telephone Company
(WP12/02 Clave pdf) Telecommunication companies depend on high availability of equipment to maintain service quality. In cellular communications electronic cards maintenance is basically reduced to exchanging parts as they fail. These parts are geographically dispersed in unmanned locations. Spares and maintenance policies are thus interrelated and tend to follow multiechelon configurations, following the architecture of the physical network. We describe the optimization of spare parts and maintenance policies performed by the Venezuelan mobile phone operator Movilnet.Mobile phone, MRO, Multi-echelon inventory systems, Spare parts optimization
Randomly Evolving Idiotypic Networks: Structural Properties and Architecture
We consider a minimalistic dynamic model of the idiotypic network of
B-lymphocytes. A network node represents a population of B-lymphocytes of the
same specificity (idiotype), which is encoded by a bitstring. The links of the
network connect nodes with complementary and nearly complementary bitstrings,
allowing for a few mismatches. A node is occupied if a lymphocyte clone of the
corresponding idiotype exists, otherwise it is empty. There is a continuous
influx of new B-lymphocytes of random idiotype from the bone marrow.
B-lymphocytes are stimulated by cross-linking their receptors with
complementary structures. If there are too many complementary structures,
steric hindrance prevents cross-linking. Stimulated cells proliferate and
secrete antibodies of the same idiotype as their receptors, unstimulated
lymphocytes die.
Depending on few parameters, the autonomous system evolves randomly towards
patterns of highly organized architecture, where the nodes can be classified
into groups according to their statistical properties. We observe and describe
analytically the building principles of these patterns, which allow to
calculate number and size of the node groups and the number of links between
them. The architecture of all patterns observed so far in simulations can be
explained this way. A tool for real-time pattern identification is proposed.Comment: 19 pages, 15 figures, 4 table
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