31,335 research outputs found

    Algorithms for determining relative star height and star height

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    AbstractLet C = {R1, …, Rm} be a finite class of regular languages over a finite alphabet Σ. Let Δ = {b1, …, bm} be an alphabet, and δ be the substitution from Δ∗ into Σ∗ such that δ(bi) = Ri for all i (1 ≤ i ≤ m). Let R be a regular language over Σ which can be defined from C by a finite number of applications of the operators union, concatenation, and star. Then there exist regular languages over Δ which can be transformed onto R by δ. The relative star height of R w.r.t. C is the minimum star height of regular languages over Δ which can be transformed onto R by δ. This paper proves the existence of an algorithm for determining relative star height. This result obviously implies the existence of an algorithm for determining the star height of any regular language

    Digraph Complexity Measures and Applications in Formal Language Theory

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    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

    Analysis of RR Lyrae Stars in the Northern Sky Variability Survey

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    We use data from the Northern Sky Variability Survey (NSVS), obtained from the first generation Robotic Optical Transient Search Experiment (ROTSE-I), to identify and study RR Lyrae variable stars in the solar neighborhood. We initially identified 1197 RRab (RR0) candidate stars brighter than the ROTSE median magnitude V = 14. Periods, amplitudes, and mean V magnitudes are determined for a subset of 1188 RRab stars with well defined light curves. Metallicities are determined for 589 stars by the Fourier parameter method and by the relationship between period, amplitude, and [Fe/H]. We comment upon the difficulties of clearly classifying RRc (RR1) variables in the NSVS dataset. Distances to the RRab stars are calculated using an adopted luminosity-metallicity relation with corrections for interstellar extinction. The 589 RRab stars in our final sample are used to study the properties of the RRab population within 5 kpc of the Sun. The Bailey diagram of period versus amplitude shows that the largest component of this sample belongs to Oosterhoff type I. Metal-rich ([Fe/H] > -1) RRab stars appear to be associated with the Galactic disk. Our metal-rich RRab sample may include a thin disk as well as a thick disk population, although the uncertainties are too large to establish this. There is some evidence among the metal-rich RRab stars for a decline in scale height with increasing [Fe/H], as was found by Layden (1995). The distribution of RRab stars with -1 < [Fe/H] < -1.25 indicates that within this metallicity range the RRab stars are a mixture of stars belonging to halo and disk populations.Comment: 68 pages, 26 figures, 9 tables, accepted to A

    From Finite Automata to Regular Expressions and Back--A Summary on Descriptional Complexity

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    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

    Correlations and Fluctuations, A Summary of Quark Matter 2002

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    Results for correlations and fluctuations presented at Quark Matter 2002 are summarized. These results include Hanbury-Brown Twiss interferometry of a wide variety of species, large scale fluctuations and correlations in ptp_t and multiplicity, and charge fluctuations and charge balance functions.Comment: published in NPA 715, page 389c (2003
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