Wayne Snyder. An O(n log n) algorithm for generating reduced sets of ground rewrite rules equivalent to a set of ground equations E. In N. Dershowitz, editor, Rewriting Techniques and Applications, 3th International Conference, LNCS. Springer-Verlag, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Curryfication. The existing algorithms for ground Knuth Bendix completion (which implicitly also compute a congruence closure) are all rather involved, and moreover either quadratic, like [PSK96] or are based on the previous use of one of the classical congruence closure algorithms on graphs [Sny89]. We believe that our cleaner formulation of congruence closure will also be useful for improving its explanation and understanding, and for applications and extensions such as the ones we have mentioned. We are currently working on the design and a first implementation of the whole DPLL(EUF ) ....

Wayne Snyder. An o(n log n) algorithm for generating reduced sets of ground rewrite rules equivalent to a set of ground equations e. In N. Dershowitz, editor, Rewriting Techniques and Applications, 3th International Conference, LNCS. Springer-Verlag, 1989.

....Curryfication. The existing algorithms for ground Knuth Bendix completion (which implicitly also compute a congruence closure) are all rather involved, and moreover either quadratic, like [PSK96] or are based on the previous use of one of the classical congruence closure algorithms on graphs [Sny89]. We believe that our cleaner formulation of congruence closure will also be useful for improving its explanation and understanding, and for applications and extensions such as the ones we have mentioned. We are currently working on the design and a first implementation of the whole DPLL(EUF ) ....

Wayne Snyder. An o(n log n) algorithm for generating reduced sets of ground rewrite rules equivalent to a set of ground equations e. In N. Dershowitz, editor, Rewriting Techniques and Applications, 3th International Conference, LNCS. Springer-Verlag, 1989.

....completion fl d 1 of fl d and the derived equality facts is computed, the derived non equality facts are added to M d and normalisation is applied, yielding M d 1 . A second instance that was implemented is for EQ as underlying equality theory. The completion of a ground TRS can be computed [9] [25] and moreover, efficient algorithms exist ( 25] Hence, EQ is an equality theory with completion. Our prototype uses narrowing [19] to compute normal E unifiers, and an optimised form of the Knuth Bendix algorithm [15] as completion procedure. The model generator operates on range restricted ....

....facts is computed, the derived non equality facts are added to M d and normalisation is applied, yielding M d 1 . A second instance that was implemented is for EQ as underlying equality theory. The completion of a ground TRS can be computed [9] 25] and moreover, efficient algorithms exist ([25]) Hence, EQ is an equality theory with completion. Our prototype uses narrowing [19] to compute normal E unifiers, and an optimised form of the Knuth Bendix algorithm [15] as completion procedure. The model generator operates on range restricted programs. The fairness condition is implemented ....

W. Snyder. Efficient ground completion: An o(n log n) algorithm for generating reduced sets of ground rewrite rules equivalent to a set of ground equations. In Proc. of the 3rd International Conference on Rewriting Techniques and Applications, 1989.

....R, as explained below. The satisfiability of the constraint C C 0 implies that Gr(R [ R 0 ) is terminating. We now show in more detail how the ground completion step can be done in (nondeterministic) time polynomial in St(R [ N ) For this, it suffices to use the congruence closure method of [21]. It is also possible to perform this step using the method of [19] This will complete a ground system in a polynomial number of rewrites. At each step, one chooses the rule r s with the smallest right hand side s that can be applied somewhere, and applies it everywhere. When a rewrite rule u ....

....is polynomial, their combined time could be exponential in the size of the original R [ N . The polynomial bound is obtained by noting that ground completion does not increase the subterm size, and the work to ground complete is polynomial in the subterm size (for example, by the method of [19] or [21]) 2 Corollary 3.21 Suppose E is a set of equations and inequations and Theta is a substitution such that E Theta is ground and Eq unsatisfiable. Then E (R 0 ; false; fi) for some fi such that Efi is Eq unsatisfiable, and there is a proof of this that can be found in nondeterministic ....

W. Snyder. Efficient ground completion: an O(nlogn) algorithm for generating reduced sets of ground rewrite rules equivalent to a set of ground equations E. In Proceedings of the 3rd International Conference on rewriting techniques and applications, pages 419--433, 1989. Lecture Notes in Computer Science, Vol. 355.

....system is noetherian, and Observation 2.1 implies that an interreduced prefix rewriting system is confluent, since it does not have any critical situations at all. Hence, we have the following result, which is actually a special case of a corresponding result for ground term rewriting systems [Sny89] Proposition 2.3. A prefix rewriting system is canonical if and only if it is interreduced. In this paper we will be concerned with certain infinite prefix rewriting systems. Following the corresponding convention for string rewriting systems [KKO96] a prefixrewriting system P on Sigma is ....

W. Snyder. Efficient ground completion: an O(n log n) algorithm for generating reduced sets of ground rewrite rules equivalent to a set of ground equations E. In N. Deshowitz, editor, Rewriting Techniques and Applications, Proceedings RTA'89, Lecture Notes in Computer Science 355, pages 419--433. Springer-Verlag, Berlin, 1989.

.... Sigma has arity n 0 and q; q 1 ; q n 2 Q, F Q is the set of final states. A is called a deterministic TA or DTA if there are no two different rules in R with the same left hand side. Note that if A is deterministic then R is a reduced set of ground rewrite rules and thus canonical [37]. Tree automata as defined above are usually also called bottom up tree automata. Acceptance for tree automata or recognizability is defined as follows. I The set of terms recognized by a TA A = Q; Sigma; R; F ) is the set T (A) f 2 T Sigma j (9q 2 F ) Gamma R q g: A set of terms ....

W. Snyder. Efficient ground completion: An O(nlogn) algorithm for generating reduced sets of ground rewrite rules equivalent to a set of ground equations E. In G. Goos and J. Hartmanis, editors, Rewriting Techniques and Applications, volume 355 of Lecture Notes in Computer Science, pages 419--433. Springer-Verlag, 1989.

....all ground terms t and s, cf [15, Section 2.4] R j= t s , t# R = s#R : A reduced set of rules R is such that for each rule l r in R, l is irreducible with respect to R n fl rg and r is irreducible with respect to R. In the case of ground rules, a reduced set of rules is also canonical [38]. It is always possible to find a reduced set of ground rewite rules that is equivalent to a given finite set of ground equations [29] Moreover, this can be done in O(n log n) time [38] 2.5 Finite Tree Automata Finite tree automata, or simply tree automata from here on, is a generalization of ....

....rg and r is irreducible with respect to R. In the case of ground rules, a reduced set of rules is also canonical [38] It is always possible to find a reduced set of ground rewite rules that is equivalent to a given finite set of ground equations [29] Moreover, this can be done in O(n log n) time [38]. 2.5 Finite Tree Automata Finite tree automata, or simply tree automata from here on, is a generalization of classical automata. Tree automata were introduced, independently, in Doner [16] and Thatcher and Wright [40] The main motivation was to obtain decidability results for the weak monadic ....

[Article contains additional citation context not shown here]

W. Snyder. Efficient ground completion: An O(nlogn) algorithm for generating reduced sets of ground rewrite rules equivalent to a set of ground equations E. In G. Goos and J. Hartmanis, editors, Rewriting Techniques and Applications, volume 355 of Lecture Notes in Computer Science, pages 419--433. Springer-Verlag, 1989.

....all ground terms t and s, cf [16, Section 2.4] R j= t s , t# R = s# R : A reduced set of rules R is such that for each rule l r in R, l is irreducible with respect to R n fl rg and r is irreducible with respect to R. In the case of ground rules, a reduced set of rules is also canonical [43]. It is always possible to find a reduced set of ground rewite rules that is equivalent to a given finite set of ground equations [32] Moreover, this can be done in O(n log n) time [43] 2.5 Finite Tree Automata Finite tree automata, or simply tree automata from here on, is a generalization ....

....and r is irreducible with respect to R. In the case of ground rules, a reduced set of rules is also canonical [43] It is always possible to find a reduced set of ground rewite rules that is equivalent to a given finite set of ground equations [32] Moreover, this can be done in O(n log n) time [43]. 2.5 Finite Tree Automata Finite tree automata, or simply tree automata from here on, is a generalization of classical automata. Tree automata were introduced, independently, in Doner [17] and Thatcher and Wright [45] The main motivation was to obtain decidability results for the weak monadic ....

[Article contains additional citation context not shown here]

W. Snyder. Efficient ground completion: An O(nlogn) algorithm for generating reduced sets of ground rewrite rules equivalent to a set of ground equations E. In G. Goos and J. Hartmanis, editors, Rewriting Techniques and Applications, volume 355 of Lecture Notes in Computer Science, pages 419--433. Springer-Verlag, 1989.

....in polynomial time. A proof of the existence of the canonical system and a polynomial time algorithm for deriving it appeared in [10, 11] Lemmas 24 and 25) although it was not stated in terms of term rewriting. Faster O(n log n) algorithms for this problem have recently been given by Snyder [16] and Fulop and V agvolgyi [7] Partial algebras are discussed in [8] Nondeterministic partial automata have been considered previously in [15] Although the approach is new, many of the essential ideas behind the results of this paper are more or less implicit in [10, 11] 2 Partial Algebras ....

....time. The system Gamma 0 is of course just Delta E , where E is the essential subalgebra of T Sigma = Gamma. This corollary appears in [10, 11] Lemmas 24 and 25) although not stated in the language of term rewrite systems. Improved algorithms have recently been obtained by Snyder [16] and Fulop and V agvolgyi [7] These algorithms run in time O(n log n) and are the fastest known algorithms for this problem. It is decidable in polynomial time whether two Sigma algebras presented by finite sets of ground equations over Sigma are isomorphic [10, 11] one tests whether all the ....

W. Snyder. Fast ground completion: an O(n log n) algorithm for generating reduced sets of ground rewrite rules equivalent to a set of ground equations. In Nachum Dershowitz, editor, Proc. Third Int. Conf. Rewriting Techniques and Applications, pages 419--433. Springer-Verlag Lect. Notes in Comput. Sci. 355, 1989.

....The straightforward reduction of the term g(f n (c) can take a number of rewrites exponential in n. However, if we apply the rules in order of size, smallest first, to all other rules, the whole system can be rewritten to a reduced system in a polynomial number of steps. In [GNP 93, Sny89] a general, polynomial time method was presented for obtaining completed ground systems. This method was based on congruence closure, and therefore did not give direct insight into the speed of completion by traditional critical pair based methods. The question remained whether a good choice of ....

W. Snyder. Efficient ground completion: an O(nlogn) algorithm for generating reduced sets of ground rewrite rules equivalent to a set of ground equations E. In Proceedings of the 3rd International Conference on rewriting techniques and applications, pages 419--433, 1989. Lecture Notes in Computer Science, Vol. 355.

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Wayne Snyder. An O(n log n) algorithm for generating reduced sets of ground rewrite rules equivalent to a set of ground equations E. In N. Dershowitz, editor, Rewriting Techniques and Applications, 3th International Conference, LNCS. Springer-Verlag, 1989.

No context found.

Wayne Snyder. An O(n log n) algorithm for generating reduced sets of ground rewrite rules equivalent to a set of ground equations E. In N. Dershowitz, editor, Rewriting Techniques and Applications, 3th International Conference, LNCS. Springer-Verlag, 1989.

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W. Snyder. EOEcient completion: an O(nlogn) algorithm for generating reduced sets of ground rewrite rules equivalent to a set of ground equations E. In N. Dershowitz, editor, Proceedings 3rd Conf. on Rewriting Techniques and Applications, pages , Springer-Verlag, Lecture Notes in Computer Science, 1989.

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W. Snyder. Efficient ground completion: an o(nlogn) algorithm for generating reduced sets of ground rewrite rules equivalent to a set of ground equations. In Proceedings of the 3rd International Conference on rewriting techniques and applications, pages 419--433, 1989. Lecture Notes in Computer Science, Vol. 355.

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