Nachum Dershowitz. Innocuous constructor-sharing combinations. In Comon [Com97], pages 202-216. Home/Search Document Details and Download
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Modular Aspects of Rewrite-Based Specifications - Gramlich (1997) (2 citations) (Correct)
....x G(A; B) A A B 9 = Both systems are terminating and confluent, and moreover R b is a non collapsing overlay system. Hence, Theorem 8 yields completeness of the disjoint union R b Phi Rw . We note that none of the previous modularity results is applicable here (including the recent ones of [3]) In particular, Rw is neither overlaying nor left linear, and R b is also not left linear. 5 Asymmetric Versions of the Syntactic Approach Example 4 Consider the disjoint TRSs R b = Phi f(x; g(x) y) f(y; y; y) Psi Rw = 8 : H(x; x) K(B) H(x; x) C K(x) x 9 = Both systems are ....
N. Dershowitz. Innocuous constructor-sharing combinations. In H. Comon, ed., Proc. 8th Int. Conf. on Rewriting Techniques and Applications (RTA'97), LNCS 1232, pp. 202--216. Springer, 1997.
Modular Aspects of Rewrite-Based Specifications - Gramlich (1998) (2 citations) (Correct)
....G(A; B) A A B 9 = Both systems are terminating and confluent, and moreover R b is a non collapsing overlay system. Hence, Theorem 5 yields completeness of the disjoint union R b Phi Rw . We note that none of the previous modularity results is applicable here (including the recent ones of [3]) In particular, Rw is neither overlaying nor left linear, and R b is also not left linear. 5 Asymmetric Versions of the Syntactic Approach Example 4. Consider the disjoint TRSs R b = Phi f(x; g(x) y) f(y; y; y) Psi Rw = 8 : H(x; x) K(B) H(x; x) C K(x) x 9 = Both systems ....
N. Dershowitz. Innocuous constructor-sharing combinations. In H. Comon, ed., Proc. 8th RTA, LNCS 1232, pp. 202--216. Springer, 1997.
Problem 59 - Originator Kurihara (Correct)
....independent of termination Remark: Left linearity is a su cient condition, as shown long ago in [RV80] In [Ohl94] it is established that con uence is modular in the presence of the weak normalization property. This result has been extended in [Rao95, Rao] for hierarchical combinations. In [Der97], some results are given when only one of the systems is terminating. There are other su cient conditions for modularity of con uence that do not require termination of the combined system even when function symbols are shared. One set of conditions, viz. persistence , relative termination , ....
Nachum Dershowitz. Innocuous constructor-sharing combinations. In Hubert Comon, editor, 8th International Conference on Rewriting Techniques and Applications, volume 1232 of Lecture Notes in Computer Science, pages 202-216, Barcelona, Spain, June 1997. SpringerVerlag.
When are Two Rewrite Systems More than None? - Dershowitz Self-citation (Dershowitz) (Correct)
.... that the right hand side of each rule is a defined symbol, not a variable or constructor) Ohlebusch, 1994a ] d) Each system is normalizing (in the sense that every term has at least one normal form) Ohlebusch, 1994a ] e) One system is terminating and left linear and the other is bright [ Dershowitz, 1997 ] This list and those in the sequel omit some known conditions that involve undecidable properties of the union. The necessity of these conditions may be seen from the following standard example [ Huet, 1980 ] g(x; x) 0 g(x; c(x) 1 a c(a) A) The upper part is not left linear; ....
....necessity of these conditions may be seen from the following standard example [ Huet, 1980 ] g(x; x) 0 g(x; c(x) 1 a c(a) A) The upper part is not left linear; the lower is not normalizing; c is a shared constructor; neither is bright. A careful analysis of why modularity fails [ Dershowitz et al. 1997 ] shows that at the crux of the problem lie certain instances soe and t of terms s and t appearing in left sides of one system such that t contains soe as a subterm, but no other defined symbols. If soe t holds in the union, but not in the one system alone, then confluence is not ....
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Nachum Dershowitz. Innocuous constructor-sharing combinations. In H. Comon, editor, Proceedings of the Eighth International Conference on Rewriting Techniques and Applications (Sitges, Spain), number 1232 in Lecture Notes in Computer Science, pages 203--216, Berlin, June 1997. Springer-Verlag.
The complete list of RTA open problems - Date April Summary (Correct)
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Nachum Dershowitz. Innocuous constructor-sharing combinations. In Comon [Com97], pages 202-216.
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