104 research outputs found
Linearly bounded infinite graphs
Linearly bounded Turing machines have been mainly studied as acceptors for
context-sensitive languages. We define a natural class of infinite automata
representing their observable computational behavior, called linearly bounded
graphs. These automata naturally accept the same languages as the linearly
bounded machines defining them. We present some of their structural properties
as well as alternative characterizations in terms of rewriting systems and
context-sensitive transductions. Finally, we compare these graphs to rational
graphs, which are another class of automata accepting the context-sensitive
languages, and prove that in the bounded-degree case, rational graphs are a
strict sub-class of linearly bounded graphs
Coinduction up to in a fibrational setting
Bisimulation up-to enhances the coinductive proof method for bisimilarity,
providing efficient proof techniques for checking properties of different kinds
of systems. We prove the soundness of such techniques in a fibrational setting,
building on the seminal work of Hermida and Jacobs. This allows us to
systematically obtain up-to techniques not only for bisimilarity but for a
large class of coinductive predicates modelled as coalgebras. By tuning the
parameters of our framework, we obtain novel techniques for unary predicates
and nominal automata, a variant of the GSOS rule format for similarity, and a
new categorical treatment of weak bisimilarity
Базовый алгоритм действия системы поддержки принятия решений
We consider two-player parity games played on transition graphs of higher order pushdown automata. They are ``game-equivalent'' to a kind of model-checking game played on graphs of the infinite hierarchy introduced recently by Caucal. Then in this hierarchy we show how to reduce a game to a graph of lower level. This leads to an effective solution and a construction of the winning strategies
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
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
Checking NFA equivalence with bisimulations up to congruence
16pInternational audienceWe introduce bisimulation up to congruence as a technique for proving language equivalence of non-deterministic finite automata. Exploiting this technique, we devise an optimisation of the classical algorithm by Hopcroft and Karp. We compare our algorithm to the recently introduced antichain algorithms, by analysing and relating the two underlying coinductive proof methods. We give concrete examples where we exponentially improve over antichains; experimental results moreover show non negligible improvements on random automata
A First Look at Rotation in Inactive Late-Type M Dwarfs
We have examined the relationship between rotation and activity in 14
late-type (M6-M7) M dwarfs, using high resolution spectra taken at the W.M.
Keck Observatory and flux-calibrated spectra from the Sloan Digital Sky Survey.
Most were selected to be inactive at a spectral type where strong H-alpha
emission is quite common. We used the cross-correlation technique to quantify
the rotational broadening; six of the stars in our sample have vsini > 3.5
km/s. Our most significant and perplexing result is that three of these stars
do not exhibit H-alpha emission, despite rotating at velocities where previous
work has observed strong levels of magnetic field and stellar activity. Our
results suggest that rotation and activity in late-type M dwarfs may not always
be linked, and open several additional possibilities including a
rotationally-dependent activity threshold, or a possible dependence on stellar
parameters of the Rossby number at which magnetic/activity "saturation" takes
place in fully convective stars.Comment: 8 pages, 4 figures, accepted for publication in Ap
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
Symbolic Backwards-Reachability Analysis for Higher-Order Pushdown Systems
Higher-order pushdown systems (PDSs) generalise pushdown systems through the
use of higher-order stacks, that is, a nested "stack of stacks" structure.
These systems may be used to model higher-order programs and are closely
related to the Caucal hierarchy of infinite graphs and safe higher-order
recursion schemes.
We consider the backwards-reachability problem over higher-order Alternating
PDSs (APDSs), a generalisation of higher-order PDSs. This builds on and extends
previous work on pushdown systems and context-free higher-order processes in a
non-trivial manner. In particular, we show that the set of configurations from
which a regular set of higher-order APDS configurations is reachable is regular
and computable in n-EXPTIME. In fact, the problem is n-EXPTIME-complete.
We show that this work has several applications in the verification of
higher-order PDSs, such as linear-time model-checking, alternation-free
mu-calculus model-checking and the computation of winning regions of
reachability games
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