RECOGNIZABLE PICTURE LANGUAGES

1992 ◽  
Vol 06 (02n03) ◽  
pp. 241-256 ◽  
Author(s):  
DORA GIAMMARRESI ◽  
ANTONIO RESTIVO
Keyword(s):  
Two Dimensional ◽  
Closure Properties ◽  
One Dimensional ◽  
New Family ◽  
The Family ◽  
Emptiness Problem ◽  
Picture Languages ◽  
Local Languages

The purpose of this paper is to propose a new notion of recognizability for picture (two-dimensional) languages extending the characterization of one-dimensional recognizable languages in terms of local languages and alphabetic mappings. We first introduce the family of local picture languages (denoted by LOC) and, in particular, prove the undecidability of the emptiness problem. Then we define the new family of recognizable picture languages (denoted by REC). We study some combinatorial and language theoretic properties of REC such as ambiguity, closure properties or undecidability results. Finally we compare the family REC with the classical families of languages recognized by four-way automata.

A CHARACTERIZATION OF RECOGNIZABLE PICTURE LANGUAGES

1994 ◽  
Vol 08 (02) ◽  
pp. 501-508 ◽  
Author(s):  
KATSUSHI INOUE ◽  
ITSUO TAKANAMI
Keyword(s):  
Finite Automata ◽  
Two Dimensional ◽  
Open Problems ◽  
Nondeterministic Finite Automata ◽  
Letter Alphabet ◽  
The Family ◽  
On Line ◽  
Picture Languages

This paper first shows that REC, the family of recognizable picture languages in Giammarresi and Restivo,3 is equal to the family of picture languages accepted by two-dimensional on-line tessellation acceptors in Inoue and Nakamura.5 By using this result, we then solve open problems in Giammarresi and Restivo,3 and show that (i) REC is not closed under complementation, and (ii) REC properly contains the family of picture languages accepted by two-dimensional nondeterministic finite automata even over a one letter alphabet.

RESTARTING TILING AUTOMATA

2013 ◽  
Vol 24 (06) ◽  
pp. 863-878 ◽  
Author(s):  
DANIEL PRŮŠA ◽  
FRANTIŠEK MRÁZ
Keyword(s):  
Regular Languages ◽  
Two Dimensional ◽  
Scanning Strategy ◽  
Closure Properties ◽  
Computing Device ◽  
New Model ◽  
Picture Languages

We present a new model of a two-dimensional computing device called restarting tiling automaton. The automaton defines a set of tile-rewriting, weight-reducing rules and a scanning strategy by which a tile to rewrite is being searched. We investigate properties of the induced families of picture languages. Special attention is paid to picture languages that can be accepted independently of the scanning strategy. We show that this family strictly includes REC and exhibits similar closure properties. Moreover, we prove that its intersection with the set of one-row languages coincides with the regular languages.

Bifurcations of one- and two-dimensional maps

1984 ◽  
Vol 311 (1515) ◽  
pp. 43-102 ◽  
Keyword(s):  
Periodic Orbits ◽  
Period Doubling ◽  
Jacobian Determinant ◽  
Two Dimensional ◽  
Hénon Map ◽  
Stable And Unstable Manifolds ◽  
Henon Map ◽  
One Dimensional ◽  
The Family ◽  
Area Preserving

We study the qualitative dynamics of two-parameter families of planar maps of the form F^e(x, y) = (y, -ex+f(y)), where f :R -> R is a C 3 map with a single critical point and negative Schwarzian derivative. The prototype of such maps is the family f(y) = u —y 2 or (in different coordinates) f(y) = Ay(1 —y), in which case F^ e is the Henon map. The maps F e have constant Jacobian determinant e and, as e -> 0, collapse to the family f^. The behaviour of such one-dimensional families is quite well understood, and we are able to use their bifurcation structures and information on their non-wandering sets to obtain results on both local and global bifurcations of F/ ue , for small e . Moreover, we are able to extend these results to the area preserving family F/u. 1 , thereby obtaining (partial) bifurcation sets in the (/u, e)-plane. Among our conclusions we find that the bifurcation sequence for periodic orbits, which is restricted by Sarkovskii’s theorem and the kneading theory for one-dimensional maps, is quite different for two-dimensional families. In particular, certain periodic orbits that appear at the end of the one-dimensional sequence appear at the beginning of the area preserving sequence, and infinitely many families of saddle node and period doubling bifurcation curves cross each other in the ( /u, e ) -parameter plane between e = 0 and e = 1. We obtain these results from a study of the homoclinic bifurcations (tangencies of stable and unstable manifolds) of F /u.e and of the associated sequences of periodic bifurcations that accumulate on them. We illustrate our results with some numerical computations for the orientation-preserving Henon map.

scholarly journals SEM characterization of two-dimensional patterns generated in titanium by femtosecond laser interferometry

2013 ◽  
Vol 19 (S4) ◽  
pp. 143-144
Author(s):  
V. Oliveira ◽  
N.I. Polushkin ◽  
O. Conde ◽  
R. Vilar
Keyword(s):  
Laser Radiation ◽  
Femtosecond Laser ◽  
Repetition Rate ◽  
Pulse Repetition Rate ◽  
Two Dimensional ◽  
Femtosecond Laser Radiation ◽  
Scanning Velocity ◽  
One Dimensional ◽  
Scanning Electron

Laser ablation using ultrafast femtosecond lasers and holographic schemes has proven to be a powerful and versatile tool for surface and volume structuring. The principle of operation of this technique is simple: when two or more pulses overlap in time and space, an interference pattern is generated that can be used to create periodic surface structures. In addition, due to the extremely short pulse duration, a very high peak power is achieved leading to intense non-linear effects. As a result, almost any type of material can be processed without undesirable collateral thermal effects.In this paper, characterization of two-dimensional (2D) patterns generated in titanium using femtosecond laser radiation has been carried out using scanning electron microscopy (SEM). The laser source is a commercial Yb:KYW laser system providing pulses with a duration of 560 fs at a central wavelength of >= 1030 nm. The surface topography was characterized using a Hitachi S2400 scanning electron microscope operated at an electron acceleration voltage of 25.0 kV. Laser processing was performed in air on polished grade 2 titanium samples, a material typically used in low load bearing medical devices.One-dimensional (1D) gratings were created using a modified Michelson interferometer described in detail elsewhere (Oliveira et al., 2012). To create 2D gratings a double exposure method was used. First, 1D gratings were produced in linear tracks by translating the sample relatively to the stationary interfering laser beams with a fixed scanning velocity of 0.1 mm/s. As an example, Figure 1 depicts SEM pictures of horizontal and vertical 1D gratings with period of about 3.9 m, generated using a pulse energy and pulse repetition rate of 0.35 mJ and 100 Hz, respectively. The peak to valley distance of these patterns can be controlled either by changing the scanning velocity or the pulse repetition rate. By overlapping two linear tracks, different kinds of 2D structures can be created. Figure 2 depicts a square pattern obtained by overlapping two 1D gratings rotated by 90°. The dimensions of the squares depend on the one-dimensional gratings period, which in turn can be easily controlled by varying the distance between the interfering beams. Figure 3 depicts two other possibilities: i) trapezium-like patterns obtained by rotating the 1D gratings by 45°, and ii) rectangular patterns obtained using 1D gratings with different periods and rotated by 90°.The proposed optical setup offers a simple method of texturing the surface of materials and, hence, to control surface properties such as wettability. In the case of titanium, this is particularly important because surface texturing enhances its osseointegration ability. For this purpose, when compared with the columns spontaneously formed on titanium surfaces treated with femtosecond laser radiation, these 2D gratings present the major advantage of being size and shape-controllable.

One- and two-dimensional PbII compounds resulting from reaction of PbBr2 and Pb(SCN)2 with pyrimidine-2-thione

2021 ◽  
Vol 77 (7) ◽  
Author(s):  
Vânia Denise Schwade ◽  
Bárbara Tirloni
Keyword(s):  
Structural Characterization ◽  
Diffuse Reflectance ◽  
Tautomeric Form ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
One Dimensional ◽  
X Ray ◽  
Ft Ir ◽  
Compound Ii

Pyrimidine-2-thione (HSpym) reacts with lead(II) thiocyanate and lead(II) bromide in N,N-dimethylformamide (DMF) to form poly[(μ-isothiocyanato-κ2 N:S)(μ4-pyrimidine-2-thiolato-κ6 N 1,S:S:S:S,N 3)lead(II)], [Pb(C4H3N2S)(NCS)] n or [Pb(Spym)(NCS)] n , (I), and the polymeric one-dimensional (1D) compound catena-poly[[μ4-bromido-di-μ-bromido-(μ-pyrimidine-2-thiolato-κ3 N 1,S:S)(μ-pyrimidine-2-thione-κ3 N 1,S:S)dilead(II)] N,N-dimethylformamide monosolvate], {[Pb2Br3(C4H3N2S)(C4H4N2S)]·C3H7NO} n or {[Pb2Br3(Spym)(HSpym)]·DMF} n , (IIa), respectively. Poly[μ4-bromido-di-μ3-bromido-(μ-pyrimidine-2-thiolato-κ3 N 1,S:S)(μ-pyrimidine-2-thione-κ3 N 1,S:S)dilead(II)], [Pb2Br3(C4H3N2S)(C4H4N2S)] n or [Pb2Br3(Spym)(HSpym)] n , (IIb), could be obtained as a mixture with (IIa) when using a lesser amount of solvent. In the crystal structures of the pseudohalide/halide PbII stable compounds, coordination of anionic and neutral HSpym has been observed. Both Spym− (in the thiolate tautomeric form) and NCS− ligands were responsible for the two-dimensional (2D) arrangement in (I). The Br− ligands establish the 1D polymeric arrangement in (IIa). Eight-coordinated metal centres have been observed in both compounds, when considering the Pb...S and Pb...Br interactions. Both compounds were characterized by FT–IR and diffuse reflectance spectroscopies, as well as by powder X-ray diffraction. Compound (IIa) and its desolvated version (IIb) represent the first structurally characterized PbII compounds containing neutral HSpym and anionic Spym− ligands. After a prolonged time in solution, (IIa) is converted to another compound due to complete deprotonation of HSpym. The structural characterization of (I) and (II) suggests HSpym as a good candidate for the removal of PbII ions from solutions containing thiocyanate or bromide ions.

scholarly journals Iterative arrays with self-verifying communication cell

2020 ◽  
Author(s):  
Martin Kutrib
Keyword(s):  
Cellular Automata ◽  
Time Complexity ◽  
Input Word ◽  
Closure Properties ◽  
Multiplicative Factor ◽  
Computational Capacity ◽  
The Family ◽  
Computation Path

Abstract We study the computational capacity of self-verifying iterative arrays ($${\text {SVIA}}$$ SVIA ). A self-verifying device is a nondeterministic device whose nondeterminism is symmetric in the following sense. Each computation path can give one of the answers yes, no, or do not know. For every input word, at least one computation path must give either the answer yes or no, and the answers given must not be contradictory. It turns out that, for any time-computable time complexity, the family of languages accepted by $${\text {SVIA}}$$ SVIA s is a characterization of the so-called complementation kernel of nondeterministic iterative array languages, that is, languages accepted by such devices whose complementation is also accepted by such devices. $${\text {SVIA}}$$ SVIA s can be sped-up by any constant multiplicative factor as long as the result does not fall below realtime. We show that even realtime $${\text {SVIA}}$$ SVIA are as powerful as lineartime self-verifying cellular automata and vice versa. So they are strictly more powerful than the deterministic devices. Closure properties and various decidability problems are considered.

Context-sensitive languages and G-automata

2017 ◽  
Vol 27 (02) ◽  
pp. 237-249
Author(s):  
Rachel Bishop-Ross ◽  
Jon M. Corson ◽  
James Lance Ross
Keyword(s):  
Word Problem ◽  
Finitely Generated ◽  
Closure Properties ◽  
Finitely Generated Group ◽  
Context Sensitive ◽  
The Family

For a given finitely generated group [Formula: see text], the type of languages that are accepted by [Formula: see text]-automata is determined by the word problem of [Formula: see text] for most of the classical types of languages. We observe that the only exceptions are the families of context-sensitive and recursive languages. Thus, in general, to ensure that the language accepted by a [Formula: see text]-automaton is in the same classical family of languages as the word problem of [Formula: see text], some restriction must be imposed on the [Formula: see text]-automaton. We show that restricting to [Formula: see text]-automata without [Formula: see text]-transitions is sufficient for this purpose. We then define the pullback of two [Formula: see text]-automata and use this construction to study the closure properties of the family of languages accepted by [Formula: see text]-automata without [Formula: see text]-transitions. As a further consequence, when [Formula: see text] is the product of two groups, we give a characterization of the family of languages accepted by [Formula: see text]-automata in terms of the families of languages accepted by [Formula: see text]- and [Formula: see text]-automata. We also give a construction of a grammar for the language accepted by an arbitrary [Formula: see text]-automaton and show how to get a context-sensitive grammar when [Formula: see text] is finitely generated with a context-sensitive word problem and the [Formula: see text]-automaton is without [Formula: see text]-transitions.

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