Dershowitz, N., Jouannaud, J. P., and Klop, J. W. (1995), Problems in rewriting III, in "Rewriting Techniques and Applications '95," Lecture Notes in Computer Science, Vol. 914, pp. 457--471, Springer-Verlag, Berlin/New York.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....as in the multiple rule case. We conjecture that in the construction presented above we indeed have that termination of E(RP ) implies total termination of E(RP ) Together with the above equivalences this would prove undecidability of total termination for a single rule, solving problem 87 from Dershowitz et al. 1995). 6. Conclusions We proved that total termination is an undecidable property of finite term rewriting systems. We conjecture that total termination is even undecidable for a single orthogonal rewrite rule. Acknowledgements: We should like to thank Alfons Geser and Maria Ferreira for their ....

N. Dershowitz, J.-P. Jouannaud, and J.W. Klop. Problems in rewriting III. In J. Hsiang, editor, Proceedings of the 6th Conference on Rewriting Techniques and Applications, volume 914 of Lecture Notes in Computer Science, pages 457--471. Springer, 1995.

.... jma tcs.uni.wroc.pl Institute of Computer Science University of Wroc law, ul. Przesmyckiego 20 51 165 Wroc law, Poland Abstract. We show that the 9 8 part of the equational theory modulo an AC symbol is undecidable. This solves the open problem 25 from the RTA list ( DJK91] DJK93] [DJK95], RTA] We show that this result holds also for the equational theory modulo an ACI symbol. 1 Introduction Formulae built of terms and the equality predicate are one of the most natural objects in rewriting. One of the most natural ways of modeling the semantic behavior of real objects is ....

....which This paper is the extended version of [M99] Supported by Polish KBN grant 8 T11C 043 19 itself is a special case of the 2 part of the theory. Decidability of the whole 2 part was stated as an open problem in [T90] and then on the RTA list of open problems ( DJK91] DJK93] [DJK95], RTA] In this paper we present the negative solution to the problem. The rest of the paper is organized as follows: in Section 2 we prove undecidability of the existential universal ( 2 ) part of the theory of an AC idempotent symbol: we assume there is a function symbol in the signature ....

N. Dershowitz, J-P Jouannaud, J. W. Klop, Problems in Rewriting III, Proceedings of RTA 95, (Springer LNCS vol. 914) pp 457-471,

....as R. The problem whether first order theories of one step rewriting in finite systems are decidable was suggested by (Caron, Coquid e Dauchet 1993, p. 331) and repeated in the Rewriting Techniques and Applications (RTA) lists of open problems (Dershowitz, Jouannaud Klop 1993, p. 473) (Dershowitz, Jouannaud Klop 1995, p. 461) The motivation for the problem is quite natural. For example, the ground reducibility of a term t(x) and the strong confluence of a system are expressible by the formulas 8x9yR(t(x) y) and 8x; y; z9w(R(x; y) R(x; z) R(y; w) R(z; w) respectively. Note that both properties are ....

....Results The results of (Treinen 1996, Marcinkowski 1997, Vorobyov 1997) are often misinterpreted or misunderstood, and some clarification is necessary. Let us first recall the statement of the problem, as given in the RTA 93, RTA 95 lists of open problems; see (Dershowitz et al. 1993, Dershowitz et al. 1995). Problem 51 (RTA 93, RTA 95) For an arbitrary finite term rewriting system R, is the first order theory of one step rewriting R decidable . 2 This informal statement allows for at least two different interpretations, depending on the order of quantification (note that : 2) 1) ....

Dershowitz, N., Jouannaud, J. & Klop, J. (1995), Problems in rewriting III, in `Rewriting Techniques and Applications'95', Vol. 914 of Lect. Notes Comput. Sci., pp. 457--471.

....is Undecidable (Note) Sergei Vorobyov Max Planck Institut fur Informatik Im Stadtwald, D 66123, Saarbrucken, Germany (e mail: sv mpi sb.mpg.de, Phone: 49) 681 302 5436, Fax: 49) 681 302 5401) Abstract. We settle in the negative the following Problem 51 (Comon Dauchet, RTA 93 [3] RTA 95 [4]) Given an arbitrary finite term rewriting system R, is the first order theory of one step rewriting ( R ) decidable Decidability would imply the decidability of the first order theory of encompassment (that is, being an instance of a subterm) 1] as well as several known decidability results ....

N. Dershowitz, J.P. Jouannaud, and J.W. Klop. Problems in rewriting III. In Rewriting Techniques and Applications'95, volume 914 of Lect. Notes Comput. Sci., pages 457--471, 1995.

....preservation of the rewriting properties (viz derivability, termination, confluence, conservativeness) for the transformation. 1 Introduction In the last years interest in applications and theory of rewriting has been increased as can be inferred from the collection of open problems in [DJK95]. Rewriting systems are attractive because of their simple syntax and semantics, which facilitate a satisfactory mathematical analysis. Additionally, rewriting systems play a fundamental role in algebraic specification, computing in algebraic structures and theorem proving. Term rewriting systems ....

N. Dershowitz, J-P. Jouannaud, and J. W. Klop. Problems in Rewriting III. In J. Hsiang, editor, Proc. Sixth International conference on Rewriting Techniques and Applications, Kaiserslautern, Germany, volume 914 of LNCS. Springer, April 1995.

....jma tcs.uni.wroc.pl Institute of Computer Science University of Wroc law, ul. Przesmyckiego 20 51 165 Wroc law, Poland Abstract We show that the 9 8 part of the equational theory modulo an AC symbol is undecidable. This solves the open problem 25 from the RTA list ( DJK91] DJK93] [DJK95]) 0 Introduction Formulae built of terms and the equality predicate are one of the most natural objects in rewriting. One of the most natural ways of modeling the semantic behaviour of real objects is considering additional equality axioms between terms. The most natural set of equality axioms is ....

....were written about the decidability of some special cases of so called AC complement problem, which itself is a special case of the Sigma 2 part of the theory. Decidability of the whole Sigma 2 part was stated as an open problem in [T90] and then on the RTA list of open problems ( DJK91] DJK93] [DJK95]) In this paper we present the negative solution of the problem. The rest of the paper is organized as follows: in Section 2 we prove undecidability of the existential universal ( Sigma 2 ) part of the theory of an AC idempotent symbol: we assume there is a function symbol in the signature ....

N. Dershowitz, J-P Jouannaud, J. W. Klop, Problems in Rewriting III, Proceedings of RTA 95, (Springer LNCS vol. 914) pp 457-471,

....[46] on the undecidability of finiteness of Thue closure, which we give in Section 7. The first, simplest application we give is to term rewriting. In 1995 Ralf Treinen [56] proved that the first order theory of one step rewriting was undecidable, thus solving a problem stated in [9] and listed in [14, 15]. This result was independently and roughly in the same time, obtained by Sergei Vorobyov [57] The paper of Treinen has attracted considerable attention, because of the widespread belief in the decidability of the theory. In Section 3 we first show that the theorem of Treinen can be obtained as ....

....to w in one step using a rule of R. The first order theory of one step rewriting is the (first order) theory of the structure hU ; i. The problem of decidability of the first order theory of one step rewriting was stated in [9] and was included in the lists of open problems on rewriting ([14, 15]) In 1995 Ralf Treinen and Sergei Vorobyov independently proved that the theory is undecidable. The paper of Treinen [56] published in 1996 has attracted a considerable attention, since it was commonly believed that the theory was decidable. This belief was justified by the fact that many natural ....

N. Dershowitz, J. Jouannaud, and J. W. Klop. Problems in rewriting iii. In Proceedings of RTA, volume 914 of Lecture Notes in Computer Science, pages 457--471. Springer, 1995.

....Problem (PCP) The results presented in this paper are stronger because (1) we obtain the same undecidability results for (much) smaller classes of onerule TRSs, and (2) we show the undecidability of total termination for one rule (simply terminating) TRSs. The latter solves problem 87 in [4] and rectifies a conjecture in [18] The relative undecidability results in [9] are obtained by using PCP in the following way: for the lower five implications X ) Y in the termination hierarchy and for all PCP instances P a TRS is constructed that always satisfies Y and satisfies X if and only if ....

N. Dershowitz, J.-P. Jouannaud, and J.W. Klop. Problems in rewriting III. In Proc. 6th RTA, volume 914 of LNCS, pages 457--471, 1995.

....S 1 : l 1 r 1 ; S 2 : l 2 r 2 2 R and any non variable subterm l 2 =p of l 2 unless S 1 and S 2 are identical and p = ffl. For instance, R 2 in Introduction is non overlapping. One of the authors posed the problem in [22] of whether a non overlapping TRS is UN, which is Problem 79 in [7]. In [19] a partial answer is obtained: a non overlapping and depth preserving TRS is UN. 6 Verma stated in [33] that every non overlapping uniquely consistent non 6 They also show CR of a non overlapping TRS with a stronger restriction [10,11] duplicating TRS in which every non overlap ....

N. Dershowitz, J.-P. Jouannaud, and J. W. Klop. Problems in rewriting iii. In Proc. the 6th RTA, pages 457--471, 1995. A whole list on WWW at http://www.lri.fr/~rtaloop/index.html.

No context found.

Dershowitz, N., Jouannaud, J. P., and Klop, J. W. (1995), Problems in rewriting III, in "Rewriting Techniques and Applications '95," Lecture Notes in Computer Science, Vol. 914, pp. 457--471, Springer-Verlag, Berlin/New York.

No context found.

N. Dershowitz, J.P. Jouannaud, and J.W. Klop. Problems in rewriting III. In Rewriting Techniques and Applications'95, volume 914 of Lect. Notes Comput. Sci., pages 457-471, 1995.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC