133 research outputs found
Real-Time Vector Automata
We study the computational power of real-time finite automata that have been
augmented with a vector of dimension k, and programmed to multiply this vector
at each step by an appropriately selected matrix. Only one entry
of the vector can be tested for equality to 1 at any time. Classes of languages
recognized by deterministic, nondeterministic, and "blind" versions of these
machines are studied and compared with each other, and the associated classes
for multicounter automata, automata with multiplication, and generalized finite
automata.Comment: 14 page
The spatial coverage of dairy cattle urine patches in an intensively grazed pasture system
Accurate field data on the paddock area affected by cow urine depositions are critical to the estimation and modelling of nitrogen (N) losses and N management in grazed pasture systems. A new technique
using survey-grade global positioning system (GPS) technology was developed to precisely measure the paddock spatial area coverage, diversity and distribution of dairy cattle urine patches in grazed paddocks over time. A 4-year study was conducted on the Lincoln University Dairy Farm (LUDF), Canterbury, New Zealand, from 2003 to 2007. Twelve field plots, each 100m² in area, were established
on typical grazing areas of the farm. All urine and dung deposits within the plots were visually identified, the pasture response area (radius) measured and position marked with survey-grade GPS. The plots were grazed as part of the normal grazing rotation of the farm and urine and dung deposits measured at 12-week intervals. The data were collated using spatial (GIS) software and an assessment of annual urine patch coverage and spatial distribution was made. Grazing intensities ranged from
17645 to 30295 cow grazing h/ha/yr. Mean annual areas of urine patches ranged from 0·34 to 0·40m² (4-year mean 0·37±0·009m²), with small but significant variation between years and seasons. Mean annual urine patch numbers were 6240±124 patches/ha/yr. The mean proportional area coverage for a single sampling event or season was 0·058 and the mean proportional annual urine patch coverage was 0·232±0·0071. There was a strong linear relationship between annual cow grazing h/ha and urine patch numbers/ha (R²=0·69) and also annual urine patch area coverage (R²=0·77). Within the stocking densities observed in this study, an annual increase of 10 000 cow grazing h/ha increased urine patch numbers by 1800 urine patches/ha/yr and annual urine patch area coverage by 0·07. This study presents new quantitative data on urine patch size, numbers and the spatial coverage of patches on a temporal basis
The Context-Freeness Problem Is coNP-Complete for Flat Counter Systems
International audienceBounded languages have recently proved to be an important class of languages for the analysis of Turing-powerful models. For instance, bounded context-free languages are used to under-approximate the behav-iors of recursive programs. Ginsburg and Spanier have shown in 1966 that a bounded language L ⊆ a * 1 · · · a * d is context-free if, and only if, its Parikh image is a stratifiable semilinear set. However, the question whether a semilinear set is stratifiable, hereafter called the stratifiability problem, was left open, and remains so. In this paper, we give a partial answer to this problem. We focus on semilinear sets that are given as finite systems of linear inequalities, and we show that stratifiability is coNP-complete in this case. Then, we apply our techniques to the context-freeness problem for flat counter systems, that asks whether the trace language of a counter system intersected with a bounded regular language is context-free. As main result of the paper, we show that this problem is coNP-complete
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
Approximate Deadline-Scheduling with Precedence Constraints
We consider the classic problem of scheduling a set of n jobs
non-preemptively on a single machine. Each job j has non-negative processing
time, weight, and deadline, and a feasible schedule needs to be consistent with
chain-like precedence constraints. The goal is to compute a feasible schedule
that minimizes the sum of penalties of late jobs. Lenstra and Rinnoy Kan
[Annals of Disc. Math., 1977] in their seminal work introduced this problem and
showed that it is strongly NP-hard, even when all processing times and weights
are 1. We study the approximability of the problem and our main result is an
O(log k)-approximation algorithm for instances with k distinct job deadlines
On Functionality of Visibly Pushdown Transducers
Visibly pushdown transducers form a subclass of pushdown transducers that
(strictly) extends finite state transducers with a stack. Like visibly pushdown
automata, the input symbols determine the stack operations. In this paper, we
prove that functionality is decidable in PSpace for visibly pushdown
transducers. The proof is done via a pumping argument: if a word with two
outputs has a sufficiently large nesting depth, there exists a nested word with
two outputs whose nesting depth is strictly smaller. The proof uses technics of
word combinatorics. As a consequence of decidability of functionality, we also
show that equivalence of functional visibly pushdown transducers is
Exptime-Complete.Comment: 20 page
Solving Medium-Density Subset Sum Problems in Expected Polynomial Time: An Enumeration Approach
The subset sum problem (SSP) can be briefly stated as: given a target integer
and a set containing positive integer , find a subset of
summing to . The \textit{density} of an SSP instance is defined by the
ratio of to , where is the logarithm of the largest integer within
. Based on the structural and statistical properties of subset sums, we
present an improved enumeration scheme for SSP, and implement it as a complete
and exact algorithm (EnumPlus). The algorithm always equivalently reduces an
instance to be low-density, and then solve it by enumeration. Through this
approach, we show the possibility to design a sole algorithm that can
efficiently solve arbitrary density instance in a uniform way. Furthermore, our
algorithm has considerable performance advantage over previous algorithms.
Firstly, it extends the density scope, in which SSP can be solved in expected
polynomial time. Specifically, It solves SSP in expected time
when density , while the previously best
density scope is . In addition, the overall
expected time and space requirement in the average case are proven to be
and respectively. Secondly, in the worst case, it
slightly improves the previously best time complexity of exact algorithms for
SSP. Specifically, the worst-case time complexity of our algorithm is proved to
be , while the previously best result is .Comment: 11 pages, 1 figur
Reachability of Communicating Timed Processes
We study the reachability problem for communicating timed processes, both in
discrete and dense time. Our model comprises automata with local timing
constraints communicating over unbounded FIFO channels. Each automaton can only
access its set of local clocks; all clocks evolve at the same rate. Our main
contribution is a complete characterization of decidable and undecidable
communication topologies, for both discrete and dense time. We also obtain
complexity results, by showing that communicating timed processes are at least
as hard as Petri nets; in the discrete time, we also show equivalence with
Petri nets. Our results follow from mutual topology-preserving reductions
between timed automata and (untimed) counter automata.Comment: Extended versio
The Power of Centralized PC Systems of Pushdown Automata
Parallel communicating systems of pushdown automata (PCPA) were introduced in
(Csuhaj-Varj{\'u} et. al. 2000) and in their centralized variants shown to be
able to simulate nondeterministic one-way multi-head pushdown automata. A
claimed converse simulation for returning mode (Balan 2009) turned out to be
incomplete (Otto 2012) and a language was suggested for separating these PCPA
of degree two (number of pushdown automata) from nondeterministic one-way
two-head pushdown automata. We show that the suggested language can be accepted
by the latter computational model. We present a different example over a single
letter alphabet indeed ruling out the possibility of a simulation between the
models. The open question about the power of centralized PCPA working in
returning mode is then settled by showing them to be universal. Since the
construction is possible using systems of degree two, this also improves the
previous bound three for generating all recursively enumerable languages.
Finally PCPAs are restricted in such a way that a simulation by multi-head
automata is possible
Vector Bin Packing with Multiple-Choice
We consider a variant of bin packing called multiple-choice vector bin
packing. In this problem we are given a set of items, where each item can be
selected in one of several -dimensional incarnations. We are also given
bin types, each with its own cost and -dimensional size. Our goal is to pack
the items in a set of bins of minimum overall cost. The problem is motivated by
scheduling in networks with guaranteed quality of service (QoS), but due to its
general formulation it has many other applications as well. We present an
approximation algorithm that is guaranteed to produce a solution whose cost is
about times the optimum. For the running time to be polynomial we
require and . This extends previous results for vector
bin packing, in which each item has a single incarnation and there is only one
bin type. To obtain our result we also present a PTAS for the multiple-choice
version of multidimensional knapsack, where we are given only one bin and the
goal is to pack a maximum weight set of (incarnations of) items in that bin
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