On contour representation of two dimensional patterns

Abstract

Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we present the basis of a new formal representation of two-dimensional patterns based on contours and their compositions. Then, we present efficient algorithms to verify correctness of the contourrepresentation. Finally, we briefly discuss possible applications, in particular using them as a basic instrument in developing software tools for handling two dimensional words.

Self-Assembling Interactive Modules: A Research Programme

“…(3) An enriched version supporting recursion was presented in [25]. (4) Spacetime invariant (2-dimensional) regular expressions are presented in [2,3,4] and in the current paper. ( 5) Verification methods lifting Floyd and Hoare logics to 2-dimensions have been described, too.…”

“…Word composition. The solution to the problems identified in the previous paragraphs is to define a restricted composition using relevant information of the contours of the words [2,3,4], only. A few elements of interest on the contours are:…”

“…Regular expressions. A new approach for defining classes of twodimensional regular expressions has been introduced in [2,3,4]. It is based on words with arbitrary shapes and classes of restricted composition operators.…”

“…The field has got a renewed interest in 1990s, when a robust class of regular 2-dimensional languages has been identified; good surveys from that period are [14,23]. Comparisons between our approach and some known results in the area of 2-dimensional languages are included in the text below, as well as in our previous papers on a new type of 2-dimensional regular expressions to be introduced in the next section, see, e.g., [2,3,4].…”