H. A. Maurer, G. Rozenberg, and E. Welzl. Using string languages to describe picture languages. Information and Control, 54(3):155--185, 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of existential properties in picture languages D. Robilliard D. Simplot January 9, 1998 Abstract We are interested in description of set of pictures by string languages by using several semantics: segments [12], segments with blank moves [8] and pixels [10] We give a method to code the Post correspondence problem in rational picture languages in order to show the undecidability of existence of words satisfying a given property in a rational language. 1 Introduction In order to use the well known ....

....In order to use the well known tools of theory of formal languages to manipulate multidimensional objects such like pictures, we try to lead to the free monoid by describing this objects with words. This is the subject of the picture languages theory introduced by Maurer, Rozenberg and Welzl [12] who use the restricted Freeman s code to describe pictures made of segments. The aim is to assimilate a word with a sequence of orders to a plotter where the commands are limited to the four orders up , right , down and left designed respectively by the letters u, r, d and l. Thus the words ....

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H. A. Maurer, G. Rozenberg, and E. Welzl. Using string languages to describe picture languages. Information and Control, 54(3):155--185, 1982.

....1 Introduction Picture generating devices, such as iterated function systems, chain code picture grammars, turtle geometry picture grammars, cellular automata, random context picture grammars and collage grammars, specify in general infinite picture sequences or languages. See, for example, [PJS92,CD93,MRW82,PL90,EvdW99, DK99]. Although they are intended and used for modelling visible phenomena of various kinds, due to their infinity additional prerequisites are required to make the generated pictures visible. Depending on the resolution of the chosen output medium, be it a display or a printer, the generated pictures ....

Hermann A. Maurer, Grzegorz Rozenberg, and Emo Welzl. Using string languages to describe picture languages. Information and Control, 54:155--185, 1982.

....characterization of recursively enumerable languages in a pictural framework: besides the control by the next polyomino mapping, no ingredient of a non pictorial nature is used. In particular, we use no symbol or operation on symbols (as in the case of array [24] puzzle [22] picture description [20] grammars) no matching colors as in the case of Wang tiles, etc. Our computability model can be seen as a variant of an interactive visual language (IVL) in the sense of [2] 3] Thus, the result above can be interpreted as a proof of the computational completeness of IVL: the IVL is of the ....

H. A. Maurer, G. Rozenberg, E. Welzl, Using string languages to describe picture languages, Inform. Control, 54 (1982), 155 -- 185.

....1 Introduction Picture generating devices, such as iterated function systems, chain code picture grammars, turtle geometry picture grammars, cellular automata, random context picture grammars and collage grammars, specify in general in nite picture sequences or languages. See, for example, [PJS92, CD93, MRW82, PL90, EvdW99, DK99]. Although they are intended and used for modelling visible phenomena of various kinds, due to their in nity additional prerequisites are required to make the generated pictures visible. Depending on the resolution of the chosen output medium, be it a display or a printer, the generated pictures ....

Hermann A. Maurer, Grzegorz Rozenberg, and Emo Welzl. Using string languages to describe picture languages. Information and Control, 54:155-185, 1982.

.... classes of picture generating devices found in the literature, namely collage grammars [22] mutually recursive function systems (a generalised type of iterated function systemsv [2] which is also called hierarchical iterated function system; cf. 4, 27] context free chain code grammars [25], and 0L systems with turtle interpretation [28] are translated into tree based picture generators. In each case the equivalence of the traditional device and the tree based variant is shown. This establishes a sound formal basis for future work as well as for earlier work in [13, 7, 8, 10] ....

....of such a symbol twice. Different subtrees of the input tree yield different results while identical copies yield identical pictures (due to the fact that the top down tree transducer is deterministic) Pi 6 Chain code grammars In this section the notion of context free chain code grammars [25] 7 is translated into the tree based framework. Since only context free chain code grammars are considered in this paper, the attribute context free is dropped from now on. Roughly speaking, a chain code grammar is a context free string grammar generating words whose letters are interpreted as ....

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Hermann A. Maurer, Grzegorz Rozenberg, and Emo Welzl. Using string languages to describe picture languages. Information and Control, 54:155--185, 1982.

....approaches to fractal geometry, like the work by Culik II and Dube [CD90, CD91] would be interesting. 4) Moreover, one should compare collage grammars with other syntactic devices for the generation of pictures, like chain code picture languages (see, e.g. Maurer, Rozen10 berg, and Welzl [MRW82], Dassow [Das89] Kim [Kim90] graphical interpretation of L systems (see, e.g. Prusinkiewicz and Lindenmayer [PL90] and cellular automata (see, e.g. Toffoli and Margolus [TM88] ....

H.A. Maurer, G. Rozenberg, E. Welzl. Using string languages to describe picture languages. Information and Control 54, 155--185, 1982.

....in the case where A is a certain algebra over pictures. There are, in fact, several such algebras one may consider, dealing with di erent 17 sorts of pictures. For example, it is shown in [Dre00] that Lindenmayer systems with turtle interpretation [PL90] and context free chain code grammars [MRW82, DH93] are special cases of A interpreted td generators, where A is an algebra over line drawings, its central operation being the concatenation of line drawings. Another possibility (also studied in [Dre00] is to view subsets of R d as pictures and use operations which are based on the geometric ....

Hermann A. Maurer, Grzegorz Rozenberg, and Emo Welzl. Using string languages to describe picture languages. Information and Control, 54:155-185, 1982.

.... tree grammars (cf. GS97] ffl top down tree transductions (cf. e.g. Rou70, Tha70a, Eng75, GS84, GS97] and the YIELD transduction (cf. EV85] ffl algebras on truth values, strings, integer numbers, and terms (the free term algebra and the YIELD algebra) for chain code pictures (cf. [MRW82]) and turtle graphics [PL90] and for the type of pictures generated by collage grammars [HK91] and iterated function systems [Bar88, PJS92] and ffl displays for objects with string representation (strings, numbers, terms, etc. for a tree like visualization of terms, for line drawings (as ....

.... algebras (applications.lineDrawings.turtleAlgebra and applications.lineDrawings.chainCodeAlgebra) allow to generate line drawings as is usually done by the use of ET0L systems with turtle interpretation (cf. PL90] or by using context free grammars with the chain code interpretation of strings [MRW82]. In both cases, if the interpretation of strings is turned into a set of operations the central operation turns out to be the concatenation of line drawings, where a line drawing is a picture composed of unit lines that has a distinguished end point (and, implicitly, also a starting point, namely ....

H.A. Maurer, G. Rozenberg, and E. Welzl. Using string languages to describe picture languages. Information and Control, 54:155--185, 1982.

....only similarity transformations. 1 Introduction Inspired by the comparison of chain code and collage grammars in [DHT96] in this paper some further observations concerning the generative power of these two types of picture generating grammars are pointed out. A context free chain code grammar [MRW82] is a type 2 Chomsky grammar generating a language of words over the alphabet fu; d; l; r; #g. Such a word is then interpreted as a sequence of instructions to a plotter like device in order to produce a line drawing. The letters u, d, l, and r are interpreted as instructions to draw a unit ....

....the term rewrite relation P determined by P . A regular tree grammar or context free Chomsky grammar is said to be linear if every right hand side contains at most one nonterminal symbol. 3 Context free chain code picture languages In this section the notion of context free chain code grammars [MRW82] is recalled (with the addition of the symbols and #, which appeared later in the literature) For every point p = x; y) 2 Z 2 , we denote by u(p) d(p) l(p) and r(p) the points (x; y 1) x; y Gamma 1) x Gamma 1; y) and (x 1; y) respectively. Furthermore, for every a 2 fu; d; l; ....

Hermann A. Maurer, Grzegorz Rozenberg, and Emo Welzl. Using string languages to describe picture languages. Information and Control, 54:155-- 185, 1982.

....symbols ; for the empty set) for set theoretic union) for set theoretic complementation with respect to the set of all pictures over A) and and . Each star free picture expression over A defines a picture language over 1 Not to be confused with the notion of picture defined in [8]. 2 Juxtaposition and supraposition are also known as horizontal and vertical as well as row and column concatenation. A in a canonical way. For instance, given an alphabet A with two letters a and b, the expression a (a ; a ; a ; defines the set of all pictures ....

H. A. Maurer, G. Rozenberg, and E. Welzl. Using string languages to describe picture languages. Inform. and Control, 54(3):155--185, 1982.

....however. In the main part of the paper four of the well known classes of picture generating devices found in the literature, namely collage grammars [HK91] mutually recursive function systems (or hierarchical iterated function systems; cf. Bar88, CD93, PJS92] contextfree chain code grammars [MRW82], and 0L systems with turtle interpretation [PL90] are translated into tree based picture generators. In each case the equivalence of the traditional device with its tree based counterpart is shown. This establishes a sound formal basis for future work as well as for earlier work in [DKL97, ....

....of such a symbol twice. Different subtrees of the input tree yield different results while identical copies yield identical pictures (due to the fact that the top down tree transducer is deterministic) Pi 6 Chain code grammars In this section the notion of context free chain code grammars [MRW82] 6 is translated into the tree based framework. Roughly speaking, a chain code grammar is a string grammar generating words whose letters are interpreted as instructions to an imaginary plotter. The plotter reads the word from left to right and draws a sequence of unit lines according to the ....

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Hermann A. Maurer, Grzegorz Rozenberg, and Emo Welzl. Using string languages to describe picture languages. Information and Control, 54:155--185, 1982.

....the shuffle operation. Shuffle on trajectories provides a method of great flexibility to handle the operation of parallel composition of processes: from the catenation to the usual shuffle of processes. Languages consisting of trajectories are a special case of picture languages introduced in [31]. The paper is organized as follows. Section 2 is devoted to some basic definitions, notations and terminology, covering almost all the notions necessary 1 to read the paper. In Section 3 we introduce the notion of a trajectory and we define the shuffle of words and languages over sets of ....

H. A. Maurer, G. Rozenberg and E. Welzl, "Using String Languages to Describe Picture Languages", Information and Control, 3, 54, (1982) 155-185.

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H. Maurer, G. Rozenberg, and E. Welzl, Using string languages to describe picture languages, Information and Control 54 (1982), pp. 155-185.

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