76,829 research outputs found
Bond percolation on isoradial graphs: criticality and universality
In an investigation of percolation on isoradial graphs, we prove the
criticality of canonical bond percolation on isoradial embeddings of planar
graphs, thus extending celebrated earlier results for homogeneous and
inhomogeneous square, triangular, and other lattices. This is achieved via the
star-triangle transformation, by transporting the box-crossing property across
the family of isoradial graphs. As a consequence, we obtain the universality of
these models at the critical point, in the sense that the one-arm and
2j-alternating-arm critical exponents (and therefore also the connectivity and
volume exponents) are constant across the family of such percolation processes.
The isoradial graphs in question are those that satisfy certain weak conditions
on their embedding and on their track system. This class of graphs includes,
for example, isoradial embeddings of periodic graphs, and graphs derived from
rhombic Penrose tilings.Comment: In v2: extended title, and small changes in the tex
Digraph Complexity Measures and Applications in Formal Language Theory
We investigate structural complexity measures on digraphs, in particular the
cycle rank. This concept is intimately related to a classical topic in formal
language theory, namely the star height of regular languages. We explore this
connection, and obtain several new algorithmic insights regarding both cycle
rank and star height. Among other results, we show that computing the cycle
rank is NP-complete, even for sparse digraphs of maximum outdegree 2.
Notwithstanding, we provide both a polynomial-time approximation algorithm and
an exponential-time exact algorithm for this problem. The former algorithm
yields an O((log n)^(3/2))- approximation in polynomial time, whereas the
latter yields the optimum solution, and runs in time and space O*(1.9129^n) on
digraphs of maximum outdegree at most two. Regarding the star height problem,
we identify a subclass of the regular languages for which we can precisely
determine the computational complexity of the star height problem. Namely, the
star height problem for bideterministic languages is NP-complete, and this
holds already for binary alphabets. Then we translate the algorithmic results
concerning cycle rank to the bideterministic star height problem, thus giving a
polynomial-time approximation as well as a reasonably fast exact exponential
algorithm for bideterministic star height.Comment: 19 pages, 1 figur
The Millisecond Radio Sky: Transients from a Blind Single Pulse Search
We present the results of a search for transient radio bursts of between
0.125 and 32 millisecond duration in two archival pulsar surveys of
intermediate galactic latitudes with the Parkes multibeam receiver. Fourteen
new neutron stars have been discovered, seven of which belong to the recently
identified "rotating radio transients" (RRATs) class. Here we describe our
search methodology, and discuss the new detections in terms of how the RRAT
population relates to the general population of pulsars. The new detections
indicate (1) that the galactic z-distribution of RRATs in the surveys closely
resembles the distribution of pulsars, with objects up to 0.86 kpc from the
galactic plane; (2) where measurable, the RRAT pulse widths are similar to that
of individual pulses from pulsars of similar period, implying a similar beaming
fraction; and (3) our new detections span a variety of nulling fractions, and
thus we postulate that the RRATs may simply be nulling pulsars that are only
"on" for less than a pulse period. Finally, the newly discovered object PSR
J0941-39 may represent a link between pulsars and RRATs. This bizarre object
was discovered as an RRAT, but in follow-up observations often appeared as a
bright (~10 mJy) pulsar with a low nulling fraction. It is obvious therefore
that a neutron star can oscillate between being an RRAT and a pulsar.
Crucially, the sites of the RRAT pulses are coincident with the pulsar's
emission, implying that the two emission mechanisms are linked, and that RRATs
are not just pulsars observed from different orientations.Comment: 13 pages, 9 figures, accepted by MNRA
Regular Cost Functions, Part I: Logic and Algebra over Words
The theory of regular cost functions is a quantitative extension to the
classical notion of regularity. A cost function associates to each input a
non-negative integer value (or infinity), as opposed to languages which only
associate to each input the two values "inside" and "outside". This theory is a
continuation of the works on distance automata and similar models. These models
of automata have been successfully used for solving the star-height problem,
the finite power property, the finite substitution problem, the relative
inclusion star-height problem and the boundedness problem for monadic-second
order logic over words. Our notion of regularity can be -- as in the classical
theory of regular languages -- equivalently defined in terms of automata,
expressions, algebraic recognisability, and by a variant of the monadic
second-order logic. These equivalences are strict extensions of the
corresponding classical results. The present paper introduces the cost monadic
logic, the quantitative extension to the notion of monadic second-order logic
we use, and show that some problems of existence of bounds are decidable for
this logic. This is achieved by introducing the corresponding algebraic
formalism: stabilisation monoids.Comment: 47 page
From Finite Automata to Regular Expressions and Back--A Summary on Descriptional Complexity
The equivalence of finite automata and regular expressions dates back to the
seminal paper of Kleene on events in nerve nets and finite automata from 1956.
In the present paper we tour a fragment of the literature and summarize results
on upper and lower bounds on the conversion of finite automata to regular
expressions and vice versa. We also briefly recall the known bounds for the
removal of spontaneous transitions (epsilon-transitions) on non-epsilon-free
nondeterministic devices. Moreover, we report on recent results on the average
case descriptional complexity bounds for the conversion of regular expressions
to finite automata and brand new developments on the state elimination
algorithm that converts finite automata to regular expressions.Comment: In Proceedings AFL 2014, arXiv:1405.527
Boundedness in languages of infinite words
We define a new class of languages of -words, strictly extending
-regular languages.
One way to present this new class is by a type of regular expressions. The
new expressions are an extension of -regular expressions where two new
variants of the Kleene star are added: and . These new
exponents are used to say that parts of the input word have bounded size, and
that parts of the input can have arbitrarily large sizes, respectively. For
instance, the expression represents the language of infinite
words over the letters where there is a common bound on the number of
consecutive letters . The expression represents a similar
language, but this time the distance between consecutive 's is required to
tend toward the infinite.
We develop a theory for these languages, with a focus on decidability and
closure. We define an equivalent automaton model, extending B\"uchi automata.
The main technical result is a complementation lemma that works for languages
where only one type of exponent---either or ---is used.
We use the closure and decidability results to obtain partial decidability
results for the logic MSOLB, a logic obtained by extending monadic second-order
logic with new quantifiers that speak about the size of sets
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