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Modelling of Complex Software Systems: a Reasoned Overview
"... This paper is devoted to the presentation of the key concepts on which a mathematical theory of complex (industrial) systems can be based. We especially show how this formal framework can capture the realness of modern information technologies. We also present some new modelling problems that are na ..."
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This paper is devoted to the presentation of the key concepts on which a mathematical theory of complex (industrial) systems can be based. We especially show how this formal framework can capture the realness of modern information technologies. We also present some new modelling problems that are naturally emerging in the specific context of complex software systems.
Decidability of Equivalence for a Class of NonDeterministic Tree Transducers
 RAIRO INFORMATIQUE THEORETIQUE ET APPLICATIONS /THEORETICAL INFORMATICS AND APPLICATIONS
, 1994
"... In this paper, we consider nondeterministic tree transducers in the letter to letter case, that is to say tree transducers for which trees which appear in the rules are reduced to one letter in the righthand side as in the left one. We establish the decidability of equivalence for linear and nond ..."
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In this paper, we consider nondeterministic tree transducers in the letter to letter case, that is to say tree transducers for which trees which appear in the rules are reduced to one letter in the righthand side as in the left one. We establish the decidability of equivalence for linear and nondeleting topdown transducers. These results are valid in the bottomup case.
Decidability of Equivalence for Linear Letter to Letter Topdown Tree Transducers
"... . In this paper we consider non deterministic linear topdown tree transducers in the letter to letter case, that is to say tree transducers for which trees which appear in the rules are reduced to one letter in the righthand side as in the left one. We establish the decidability of equivalence for ..."
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. In this paper we consider non deterministic linear topdown tree transducers in the letter to letter case, that is to say tree transducers for which trees which appear in the rules are reduced to one letter in the righthand side as in the left one. We establish the decidability of equivalence for this class of transducers. 1 Introduction Tree transducers, which are a generalization of rational transformations in the word case (see [1], [4] for a synthesis), have been widely studied. The authors have choosed either the algebraic point of view ([2], [5]), or the machine point of view ([7], [8], [11] for instance). In the word case, the main results of decidability of equivalence are:  Equivalence is undecidable in the non deterministic case (T.Griffiths 1968).  Equivalence is decidable in the deterministic one (Bird 1973, Valiant 1974). The same results have been obtained in trees. Equivalence is, in general, undecidable in the non deterministic case. And it is decidable for:  bot...
Composition of Path Transductions
"... Abstract. We propose to study two infinite graph transformations that we respectively call bounded and unbounded path transduction. These graph transformations are based on path substitutions and graph products. When graphs are considered as automata, path transductions correspond to rational word t ..."
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Abstract. We propose to study two infinite graph transformations that we respectively call bounded and unbounded path transduction. These graph transformations are based on path substitutions and graph products. When graphs are considered as automata, path transductions correspond to rational word transductions on the accepted languages. They define strict subclasses of monadic transductions and preserve the decidability of monadic second order theory. We give a generalization of the Elgot and Mezei composition theorem from rational word transductions to path transductions.