W. Snyder. A fast algorithm for generating reduced ground rewriting systems from a set of ground equations. J. of Symbolic Computation, 15(4):415450, April 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....closure based methods (cf. e.g. 10] where the original signature is extended by fresh constants in order to name certain congruence classes. Yet, direct polynomial completion without extending signatures is also possible via a more sophisticated approach as demonstrated in [17] cf. also [20]) Next we summarize those basic results that will frequently be used in subsequent sections (cf. 17] 20] a) Any nite GTES E can be completed into a canonical GTRS R (over the same signature) in polynomial (more precisely: quadratic) time (w.r.t. the size of E) Moreover, the size of the ....

....order to name certain congruence classes. Yet, direct polynomial completion without extending signatures is also possible via a more sophisticated approach as demonstrated in [17] cf. also [20] Next we summarize those basic results that will frequently be used in subsequent sections (cf. 17] [20]) a) Any nite GTES E can be completed into a canonical GTRS R (over the same signature) in polynomial (more precisely: quadratic) time (w.r.t. the size of E) Moreover, the size of the completed system is bounded by the size of the original one: jRj jE j. b) If, by a canonical GTRS R, a ....

W. Snyder. A fast algorithm for generating reduced ground rewriting systems from a set of ground equations. Journal of Symbolic Computation, 15:415-450, 1993.

....the thesis of Dexter Kozen [Koz77] In his thesis, he gave a method based on congruence closure to solve the word problem for ground equations in polynomial time. His method was extended in [GNP 93] which gave a completion algorithm which runs in O(n 3 ) time. This was further extended in [Sny93] which improved the running time of the algorithm to O(nlog(n) However, these methods only work for the ground case, and were not extended to the general case. Our work can be seen as an extension of the congruence closure method to the non ground case. It is based on the result of [Lyn95b] ....

W. Snyder. A fast algorithm for generating reduced ground rewriting systems from a set of ground equations. Journal of Symbolic Computation, 15:415--450, 1993.

....closure to solve word problem in ground equational theories. J. Gallier, P. Narandran, D. Plaisted, S. Raatz [GNP 93] extend Kozen s techniques to generate convergent equational system equivalent to a ground set of equations. W. Snyder improves the running time of this algorithm to nlog(n) Sny93] D. Plaisted and A. Sattler Klein [PSK96] show that, with a particular strategy and with structure sharing, Knuth Bendix completion runs in polynomial time for a ground set of equations. Recently C. Lynch has shown [Lyn95] that a special form of paramodulation which does not need to copy terms ....

W. Snyder. A fast algorithm for generating reduced ground rewriting systems from a set of ground equations. Journal of Symbolic Computation, 15:415--450, 1993.

....the thesis of Dexter Kozen [Koz77] In his thesis, he gave a method based on congruence closure to solve the word problem for ground equations in polynomial time. His method was extended in [GNP 93] which gave a completion algorithm which runs in O(n 3 ) time. This was further extended in [Sny93] which improved the running time of the algorithm to O(nlog(n) However, these methods only work for the ground case, and were not extended to the general case. Our work can be seen as an extension of the congruence closure method to the non ground case. It is based on the result of [Lyn95b] ....

W. Snyder. A fast algorithm for generating reduced ground rewriting systems from a set of ground equations. Journal of Symbolic Computation, 15:415450, 1993. 20

....of Dexter Kozen [14] In his thesis, he gave a method based on congruence closure to solve the word problem for ground equations in polynomial time. His method was extended in Gallier et al. 8] which gave a completion algorithm that runs in O(n 3 ) time. This was further extended in Snyder [15], which improved the running time of the algorithm to O(nlog(n) However, these methods only work for the ground case, and were not extended to the general case. Our work can be seen as an extension of the congruence closure method to the non ground case. It is based on the result of Lynch [4] ....

Snyder, W. (1993). A fast algorithm for generating reduced ground rewriting systems from a set of ground equations. J. Symbolic Computation, 15: 415--450.

....of Dexter Kozen [14] In his thesis, he gave a method based on congruence closure to solve the word problem for ground equations in polynomial time. His method was extended in Gallier et al. 8] which gave a completion algorithm that runs in O#n 3 # time. This was further extended in Snyder [15], which improved the running time of the algorithm to O#nlog#n##. However, these methods only work for the ground case, and were not extended to the general case. Our work can be seen as an extension of the congruence closure method to the non ground case. It is based on the result of Lynch [4] ....

Snyder, W. (1993). A fast algorithm for generating reduced ground rewriting systems from a set of ground equations. J. Symbolic Computation, 15: 415--450.

....preferred by the user. This translates to relaxing the requirement that the rewrite rules be terminating, i.e. they could be non terminating. The requirement that rewriting rules be terminating has almost always been considered essential for generating a canonical system using completion [16]. A new method for generating a confluent rewriting system from nonterminating rewrite rules is a byproduct of this connection. We are not aware of any work on generating a confluent rewriting system from nonterminating rules other than a mention in [16] that Snyder s first algorithm does not ....

....a canonical system using completion [16] A new method for generating a confluent rewriting system from nonterminating rewrite rules is a byproduct of this connection. We are not aware of any work on generating a confluent rewriting system from nonterminating rules other than a mention in [16] that Snyder s first algorithm does not depend upon the ordering. The proposed reformulation of Shostak s algorithm also gives a new quadratic method (O(n 2 ) where n is the size of the ground equational system) for generating a canonical ground rewriting system from ground equations when the ....

[Article contains additional citation context not shown here]

W. Snyder, "A fast algorithm for generating reduced ground rewriting system from a set of ground equations," J. Symbolic Computation, 1992.

....proving procedures for rst order logic (with equality) that can run exponentially long for subclasses which have polynomial time decision procedures, as in the case of the Knuth Bendix ground completion procedure. Wayne Snyder proved that completion of ground equations can be done in nlog(n) Sny93] Recently C. Lynch has shown [Lyn95] that a special form of paramodulation which does not need to copy terms or literals runs in polynomial time in ground cases that include ground completion. This can be implemented in an elegant way using the notion of SOUR graph [LS95] These graphs represent ....

W. Snyder. A fast algorithm for generating reduced ground rewriting systems from a set of ground equations. Journal of Symbolic Computation, 15:415450, 1993.

....proving procedures for first order logic (with equality) that can run exponentially long for subclasses which have polynomial time decision procedures, as in the case of the Knuth Bendix ground completion procedure. Wayne Snyder proved that completion of ground equations can be done in nlog(n) Sny93] Recently C. Lynch has shown [Lyn95] that a special form of paramodulation which does not need to copy terms or literals runs in polynomial time in ground cases that include ground completion. This can be implemented in an elegant way using the notion of SOUR graph [LS95] These graphs represent ....

W. Snyder. A fast algorithm for generating reduced ground rewriting systems from a set of ground equations. Journal of Symbolic Computation, 15:415--450, 1993.

....closure to solve word problem in ground equational theories. J. Gallier, P. Narandran, D. Plaisted, S. Raatz [GNP 93] extend Kozen s techniques to generate convergent equational system equivalent to a ground set of equations. W. Snyder improves the running time of this algorithm to nlog(n) Sny93] D. Plaisted and A. Sattler Klein [PSK96] show that, with a particular strategy and with structure sharing, Knuth Bendix completion runs in polynomial time for a ground set of equations. Recently C. Lynch has shown [Lyn95] that a special form of paramodulation which does not need to copy terms ....

W. Snyder. A fast algorithm for generating reduced ground rewriting systems from a set of ground equations. Journal of Symbolic Computation, 15:415--450, 1993.

....to an equivalent canonical set. It corresponds to paramodulation in the case where all clauses are positive unit equalities. Polynomial time algorithms, based on congruence closure, have been given to convert a set of equations without variables into an equivalent canonical set in polynomial time [5, 21], but these algorithms are not Completion and do not work when the equations contain variables. Recently, it has been shown that ground completion with structure sharing is polynomial if a strategy is used which applies critical pairs in a certain order [19] In this paper, we de ne a method of ....

W. Snyder. A Fast Algorithm for Generating Reduced Ground Rewriting Systems from a Set of Ground Equations. Journal of Symbolic Computation 15 (1993) pp. 415-450.

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W. Snyder. A fast algorithm for generating reduced ground rewriting systems from a set of ground equations. J. of Symbolic Computation, 15(4):415450, April 1993.

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W. Snyder. A fast algorithm for generating reduced ground rewriting systems from a set of ground equations. Journal of Symbolic Computation, 15(7), 1993.

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W. Snyder. A fast algorithm for generating reduced ground rewriting systems from a set of ground equations. Journal of Symbolic Computation, 15(7), 1993.

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