G. Kucherov. On relationship between term rewriting systems and regular tree languages. In Book [Boo91].  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of Exercise 9. However not every recognizable tree language is the set of irreducible terms w.r.t. a rewrite system S (see Flp and Vgvlgyi [FV88] It was proved that the problem whether, given a rewrite system S as instance, the set of irreducible terms is recognizable is decidable (Kucherov [Kuc91] The problem of preservation of regularity by tree homomorphisms is not known decidable. Exercise 12 shows connections between preservation of regularity for tree homomorphisms and recognizability of sets of irreducible terms for rewrite systems. The notion of inductive reducibility (or ground ....

G. A. Kucherov. On relationship between term rewriting systems and regular tree languages. In R. Book, editor, Proceedings. Fourth International Conference on Rewriting Techniques and Applications, volume 488 of Lecture Notes in Computer Science, pages 299311, April 1991.

....is not modular. The question remains: Is UN a modular property of left linear term rewriting systems Problem 7 (H. Comon, M. Dauchet) Is it possible to decide whether the set of ground normal forms with respect to a given (finite) term rewriting system is a regular tree language See [34, 62]. Problem 8 (A. Middeldorp) Is the decidability of strong sequentiality for orthogonal term rewriting systems NP complete See [39, 58] Problem 9 (A. Middeldorp) Thatte [87] showed that an orthogonal constructor based rewrite system is left sequential if and only if it is strongly sequential. ....

G. Kucherov. On relationship between term rewriting systems and regular tree languages. In R. Book, editor, Proceedings of the Fourth International Conference on Rewriting Techniques and Applications, Como, Italy, Apr. 1991. In Lecture Notes in Computer Science, Springer, Berlin.

....BRA project 6454: Confer. Some progress has been made in [ Berarducci and Bohm, 1992 ] Problem 7 (H. Comon, M. Dauchet) Is it possible to decide whether the set of ground normal forms with respect to a given (finite) term rewriting system is a regular tree language See [Gilleron, 1991; Kucherov, 1991] This has been answered in the affirmative [ V agvolgyi and Gilleron, 1992; Kucherov and Tajine, 1993; Hofbauer and Huber, 1993 ] Problem 20 (Y. M etivier [ 1985 ] What is the best bound on the length of a derivation for a one rule length preserving string rewriting (semi Thue) system Is ....

....of an atomic constraint by some kind of automaton (closed under the usual Boolean operations) it is possible to solve arbitrary quantifier free constraints. This technique has been widely used extensively in the past few years [ Dauchet et al. 1990; Dauchet and Tison, 1990; Gilleron, 1991; Kucherov, 1991; Kucherov and Tajine, 1993; Gilleron et al. 1993; Caron et al. 1993 ] Concurrency Confluent systems, in general, and orthogonal ones, in particular, are natural candidates for parallel processing, since rewrites at different positions are more or less independent of each other. Work is being ....

G. Kucherov. On relationship between term rewriting systems and regular tree languages. In Ron Book, editor, Proceedings of the Fourth International Conference on Rewriting Techniques and Applications (Como, Italy), volume 488 of Lecture Notes in Computer Science, pages 299--311, Berlin, April 1991. Springer-Verlag.

....Thus, when a set is linearizable in the sense of Theorem 1, the set of instances is regular. On the other hand, if a set is not linearizable, it can be shown using a pumping lemma argument that the set of instances is not regular. This is however not easy to prove, but follows from the work [Kuc91] that we will survey below. We summarize the discussion in the following statement. Proposition 2. In the tree case, P2.1 and P2.2 are co NP complete problems. Now let us skip problem P3 for a moment and turn to problem P4 which has now a more than ten years history. The problem, known under the ....

....Proposition 3. In the tree case, P3 and P4 are both decidable problems. P3 is co NP complete and P4 is EXPTIME complete. Finally, let us turn to problems 5.1 and 5.2. Problem 5.1 has been proved decidable in [Pla85,KNZ87] Concerning Problem 5. 2, the following Theorem has been proved in [Kuc91]. Theorem 4. For a set of patterns S, Cont(S) is a regular tree language i there exists a set of linear patterns S lin such that Cont(S) Cont(S lin ) Moreover, if such a set S lin exists, it can be obtained by instantiating the non linear variables in the patterns of S by terms. Theorem 4 ....

G. A. Kucherov. On relationship between term rewriting systems and regular tree languages. In R. V. Book, editor, Proceedings 4th Conference on Rewriting Techniques and Applications, Como (Italy), volume 488 of Lecture Notes in Computer Science, pages 299-311. Springer-Verlag, April 1991.

.... system with the set of left hand sides of the rules) On the other hand, we show that the latter condition is implied by another one, namely the existence of a left linear term rewriting system L such that Red(R) Red(L) This jlinearizability propertyj was studied by one of the authors in [Kucherov, 1991] and proved equivalent to the regularity of Red(R) In this paper we give a shorter proof of this result that uses a well known Ramsey s theorem. Combining these results with the decidability of nite irreducibility, we prove the decidability of the regularity of ground normal form languages. This ....

....is not taken into account. Now we relate the property of regularity of the set of reducible ground terms to that of nite irreducibility. It is the latter property that we will actually test afterwards. The results of the rest of the section are based on the results proved by one of the authors in [Kucherov, 1991] without using explicitly the nite irreducibility property. Furthermore, we present here a new proof of the main proposition (theorem 4 below) that uses a more general technique. In particular, the well known theorem of Ramsey is used. We need the following technical lemma. Lemma 1 Let t 2 T ....

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G. A. Kucherov. On relationship between term rewriting systems and regular tree languages. In R. V. Book, editor, Proceedings 4th Conference on Rewriting Techniques and Applications, Como (Italy), volume 488 of Lecture Notes in Computer Science, pages 299311. Springer-Verlag, April 1991.

....classes are considered as well. Furthermore, various characterizations of the regular top context free languages are given, among others by means of restricted regular expressions. 1 Introduction This paper is motivated by our previous work on tree languages related to termrewriting systems [11, 7, 10]. It is well known that for a left linear term rewriting system R, the set Red(R) of ground terms reducible by R is a regular tree language. Conversely, if Red(R) is regular, then R can eoeectively be ilinearizedj, i.e. a nite language can be substituted for its non linear variables without ....

G. A. Kucherov. On relationship between term rewriting systems and regular tree languages. In 4th Conference on Rewriting Techniques and Applications, LNCS 488, pp. 299311. Springer-Verlag, 1991.

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G. Kucherov. On relationship between term rewriting systems and regular tree languages. In Book [Boo91].

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G. A. Kucherov. On relationship between term rewriting systems and regular tree languages. In R. Book, editor, Proceedings. Fourth International Conference on Rewriting Techniques and Applications, volume 488 of Lecture Notes in Computer Science, pages 299311, April 1991.

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G. A. Kucherov. On relationship between term rewriting systems and regular tree languages. In R. Book, editor, Proceedings. Fourth International Conference on Rewriting Techniques and Applications, volume 488 of Lecture Notes in Computer Science, pages 299311, April 1991.

No context found.

G. A. Kucherov. On relationship between term rewriting systems and regular tree languages. In R. Book, editor, Proceedings. Fourth International Conference on Rewriting Techniques and Applications, volume 488 of Lecture Notes in Computer Science, pages 299311, April 1991.

No context found.

G. A. Kucherov. On relationship between term rewriting systems and regular tree languages. In R. Book, editor, Proceedings. Fourth International Conference on Rewriting Techniques and Applications, volume 488 of Lecture Notes in Computer Science, pages 299311, April 1991.

No context found.

G. A. Kucherov. On relationship between term rewriting systems and regular tree languages. In R. Book, editor, Proceedings. Fourth International Conference on Rewriting Techniques and Applications, volume 488 of Lecture Notes in Computer Science, pages 299311, April 1991.

No context found.

G. A. Kucherov. On relationship between term rewriting systems and regular tree languages. In R. Book, editor, Proceedings. Fourth International Conference on Rewriting Techniques and Applications, volume 488 of Lecture Notes in Computer Science, pages 299311, April 1991.

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