Abstract
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{#} where # is a boundary symbol which surrounds the pictures. Then they define the class of recognizable picture languages as the set of languages which can be obtained by projection of a local one. This class is of interest since it admits several quite different characterizations [3]. Here, we define the hv-local picture languages where 2 × 2 tiles are replaced by horizontal and vertical dominoes. So the horizontal and the vertical scanning can be done separately. However, we prove that every recognizable picture language can be obtained as a projection of a hv-local language.
doi:10.1016/j.tcs.2007.01.019 
Copyright © 2007 Elsevier Ltd All rights reserved.
Ina Mäurer
, a, 
Received 3 February 2006;
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Abstract
The theory of two-dimensional languages as a generalization of formal string languages was motivated by problems arising from image processing and pattern recognition, and also concerns models of parallel computing. Here we investigate power series on pictures. These are functions that map pictures to elements of a semiring and provide an extension of two-dimensional languages to a quantitative setting. We assign weights to different devices, ranging from picture automata to tiling systems. We will prove that, for commutative semirings, the behaviours of weighted picture automata are precisely alphabetic projections of series defined in terms of rational operations, and also coincide with the families of series characterized by weighted tiling or weighted domino systems.
Keywords: Picture series; Two-dimensional languages; Unambiguity; Automata
