SIROMONEY ARRAY GRAMMARS AND APPLICATIONS

The Siromoney matrix model is a simple and elegant model for describing two-dimensional digital picture languages. The notion of attaching indices to nonterminals in a generative grammar, introduced and investigated by Aho. is considered in the vertical phase of a Siromoney matrix grammar (SMG). The advantage of this study is that the new model retains the simplicity and elegance of SMG but increases the generative power and enables us to describe pictures not generable by SMG. Besides certain closure properties and hierarchy results. applications of these two-dimensional grammars to describe tilings, polyominoes, distorted patterns and parquet deformations are studied.

Download Full-text

RESTARTING TILING AUTOMATA

International Journal of Foundations of Computer Science ◽

10.1142/s0129054113400236 ◽

2013 ◽

Vol 24 (06) ◽

pp. 863-878 ◽

Cited By ~ 4

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.

Download Full-text

Quantum gravity as a multitrace matrix model

International Journal of Modern Physics A ◽

10.1142/s0217751x17501809 ◽

2017 ◽

Vol 32 (31) ◽

pp. 1750180

Author(s):

Badis Ydri ◽

Cherine Soudani ◽

Ahlam Rouag

Keyword(s):

Quantum Gravity ◽

Matrix Models ◽

Large Class ◽

Matrix Model ◽

Two Dimensions ◽

Two Dimensional ◽

Topology Change ◽

New Model ◽

And Topology ◽

Emergent Geometry

We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of two-dimensional quantum gravity which works away from two dimensions and captures a large class of spaces admitting a finite spectral triple. These multitrace matrix models sustain emergent geometry as well as growing dimensions and topology change.

Download Full-text

RECOGNIZABLE PICTURE LANGUAGES

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s021800149200014x ◽

1992 ◽

Vol 06 (02n03) ◽

pp. 241-256 ◽

Cited By ~ 80

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.

Download Full-text

Multiple phases in a generalized Gross-Witten-Wadia matrix model

Journal of High Energy Physics ◽

10.1007/jhep09(2020)081 ◽

2020 ◽

Vol 2020 (9) ◽

Cited By ~ 2

Author(s):

Jorge G. Russo ◽

Miguel Tierz

Keyword(s):

Partition Function ◽

Matrix Models ◽

Characteristic Polynomial ◽

Matrix Model ◽

Phase Structure ◽

Unitary Matrix ◽

Two Dimensional ◽

Toeplitz Determinants ◽

Dimensional Parameter ◽

Planar Limit

Abstract We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed Cauchy ensemble. Exact formulas for the partition function and Wilson loops are given in terms of Toeplitz determinants and minors and large N results are obtained by using Szegö theorem with a Fisher-Hartwig singularity. In the large N (planar) limit with two scaled couplings, the theory exhibits a surprisingly intricate phase structure in the two-dimensional parameter space.

Download Full-text

Divergent ⇒ complex amplitudes in two dimensional string theory

Journal of High Energy Physics ◽

10.1007/jhep02(2021)086 ◽

2021 ◽

Vol 2021 (2) ◽

Author(s):

Ashoke Sen

Keyword(s):

Scattering Amplitudes ◽

String Theory ◽

Matrix Model ◽

Two Dimensional ◽

Full Matrix ◽

Instanton Contribution ◽

The Matrix ◽

Theory Result ◽

The One ◽

Remarkable Agreement

Abstract In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order. The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges. We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies. We also show analytically that the imaginary parts of the string theory amplitudes computed this way reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings.

Download Full-text