Narendran, Rusinowitch, and Verma. RPO constraint solving is in NP. In CSL: 12th Workshop on Computer Science Logic, volume 1584, pages 385-398. LNCS, Springer-Verlag, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....mainly used in automated deduction: the Knuth Bendix orders [9] and various versions of the recursive path orders [5] Because of its importance, the decision problem for ordering constraints has been well studied. For the recursive path orders decidability and complexity issues were considered in [8, 2, 16, 17, 15, 14]. For the Knuth Bendix orders we have the following results: the decidability of constraints [10] a nondeterministic polynomial time algorithm for constraint solving [11] a polynomial time algorithm for solving constraints consisting of a single inequality [12] In resolution based theorem ....

Narendran, Rusinowitch, and Verma. RPO constraint solving is in NP. In CSL: 12th Workshop on Computer Science Logic, volume 1584, pages 385-398. LNCS, Springer-Verlag, 1998.

.... [7] For extended signatures, decidability was shown for LPO in [17] and for RPO in [14] Regarding complexity, NP algorithms for LPO (fixed and extended signatures) and RPO (extended ones) were given in [14] More recently, an NP algorithm has been given as well for RPO under fixed signatures in [13]. NP hardness of the satisfiability problem is known, even for one single inequation, for all these cases [3] All these decision procedures use at some point the fact that a constraint C can be effectively expressed as an equivalent disjunction of expressions s 1 t 1 : s n t n , called ....

....some new variable x, which is equivalent w.r.t. satisfiability under extended signatures. This gives some intuition why this notion of solved form needs to be refined and, in particular, why transitivity through variables needs to be considered. On the other hand, the NP algorithms of [14] and [13] are not very useful in practice, since they are based on a first very expensive guess of a simple system for C, a particular constraint S of the form s n #n s n Gamma1 #n Gamma1 : # 1 s 0 , where each # i is either = or , and fsn ; s 0 g is the set of all subterms of C. In [14] it is ....

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P. Narendran, M. Rusinowitch, and R. Verma. RPO constraint solving is in NP. In G. Gottlob, E. Grandjean, and Katrin Seyr, editors, 12th Int. Conference of the European Association of Computer Science Logic (CSL'98), LNCS 1584, pages 385--398, Brno, Czech Republic, August 23--28, 1999. Springer-Verlag.

....The satisfiability problem for ordering constraints was first shown decidable for the well known recursive path orderings (RPO) introduced by N. Dershowitz [Der82] for fixed signatures [Com90,JO91] and extended ones [NR95,Nie93] NP algorithms (fixed and extended signatures) were given in [Nie93,NRV99]. For the Knuth Bendix ordering (KBO) this result has only recently been obtained (for fixed signatures) in [KV00] Ordered strategies and ordering constraint inheritance can be used without loosing completeness with built in algebraic theories E, like AC [NR97,Vig94] or AG [GN00] An additional ....

P. Narendran, M. Rusinowitch, and R. Verma. RPO constraint solving is in NP. In G. Gottlob, E. Grandjean, and Katrin Seyr, editors, 12th Int. Conference of the European Association of Computer Science Logic (CSL'98), LNCS 1584, pages 385--398, Brno, Czech Republic, August 23--28, 1999. SpringerVerlag.

.... extended signatures, decidability was shown for LPO in [NR95] and for RPO in [Nie93] Regarding complexity, NP algorithms for LPO (fixed and extended signatures) and RPO (extended ones) were given in [Nie93] More recently, an NP algorithm has been given as well for RPO under fixed signatures in [NRV99]. NPhardness of the satisfiability problem is known, even for one single inequation, for all these cases [CT94] All these decision procedures use at some point the fact that a constraint C can be effectively expressed as an equivalent disjunction of expressions s 1 t 1 : s n t n , ....

....some new variable x, which is equivalent w.r.t. satisfiability under extended signatures. This gives some intuition why this notion of solved form needs to be refined and, in particular, why transitivity through variables needs to be considered. On the other hand, the NP algorithms of [Nie93] and [NRV99] are not very useful in practice, since they are based on a first very expensive guess of a simple system for C, a particular constraint S of the form s n #n s n Gamma1 #n Gamma1 : # 1 s 0 , where each # i is either = or , and fs n ; s 0 g is the set of all subterms of C. In [Nie93] ....

[Article contains additional citation context not shown here]

P. Narendran, M. Rusinowitch, and R. Verma. RPO constraint solving is in NP. In G. Gottlob, E. Grandjean, and Katrin Seyr, editors, 12th Int. Conference of the European Association of Computer Science Logic (CSL'98), LNCS 1584, pages 385--398, Brno, Czech Republic, August 23--28, 1999. Springer-Verlag.

.... shown for LPO in [Nieuwenhuis and Rubio 1995] and for RPO in [Nieuwenhuis 1993] Regarding complexity, NP algorithms for LPO (fixed and extended signatures) and RPO (extended ones) were given in [Nieuwenhuis 1993] Recently, an NP algorithm has been given as well for RPO under fixed signatures in [Narendran, Rusinowitch and Verma 1998]. For the AC RPO ordering of [Rubio and Nieuwenhuis 1995] decidability was shown in [Comon, Nieuwenhuis and Rubio 1995] NP hardness of the satisfiability problem is known, even for one single inequation, for all these cases [Comon and Treinen 1994] All these decision procedures use at some ....

....a local analysis of the inequations considered independently. In fact any constraint s t can be expressed as the solved form s xx t, for some new variable x, which is equivalent w.r.t. satisfiability under extended signatures. On the other hand, the NP algorithms of [Nieuwenhuis 1993] and [Narendran et al. 1998] are based on a first non deterministic guess of a simple system for C, a particular constraint S of the form s n #n s n Gamma1 #n Gamma1 : # 1 s 0 , where each # i is either = or , and fs n ; s 1 g is the set of all subterms of C. Then, roughly, C is satisfiable if, and only if, some ....

Narendran P., Rusinowitch M. and Verma R. [1998], RPO constraint solving is in NP, in G. Gottlob, E. Grandjean and K. Seyr, eds, `12th Int. Conference of the European Association of Computer Science Logic (CSL)', LNCS 1584, Springer-Verlag, Brno, Czech Republic.

.... extended signatures, decidability was shown for LPO in [NR95] and for RPO in [Nie93] Regarding complexity, NP algorithms for LPO (fixed and extended signatures) and RPO (extended ones) were given in [Nie93] Very recently, an NP algorithm has been given as well for RPO under fixed signatures in [NRV98]. NP hardness of the satisfiability problem is known, even for one single inequation, for all these cases [CT94] All these decision procedures use at some point the fact that a constraint C can be effectively expressed as an equivalent disjunction of expressions s 1 t 1 : sn t n , called ....

....equivalent (under extended sigantures) solved form s xx t, for some new variable x. This gives some intuition why this notion of solved form needs to be refined and, in particular, why transitivity through variables needs to be considered. On the other hand, the NP algorithms of [Nie93] and [NRV98] are not very useful in practice, since they are based on a first very expensive guess of a simple system for C, a particular constraint S of the form s n #n s n Gamma1 #n Gamma1 : # 1 s 0 , where each # i is either = or , and fs n ; s 1 g is the set of all subterms of C. In [Nie93] ....

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P. Narendran, M. Rusinowitch, and R. Verma. RPO constraint solving is in NP. In CSL 98, Brno, Czech Republic, August 23--28, 1998. Abstract at http://www.dbai.tuwien.ac.at/CSL98.

.... extended signatures, decidability was shown for LPO in [NR95] and for RPO in [Nie93] Regarding complexity, NP algorithms for LPO (fixed and extended signatures) and RPO (extended ones) were given in [Nie93] Very recently, an NP algorithm has been given as well for RPO under fixed signatures in [NRV98]. NP hardness of the satisfiability problem is known, even for one single inequation, for all these cases [CT94] All these decision procedures use at some point the fact that a constraint C can be effectively expressed as an equivalent disjunction of expressions s 1 t 1 : s n t n , ....

....equivalent (under extended sigantures) solved form s x x t, for some new variable x. This gives some intuition why this notion of solved form needs to be refined and, in particular, why transitivity through variables needs to be considered. On the other hand, the NP algorithms of [Nie93] and [NRV98] are not very useful in practice, since they are based on a first very expensive guess of a simple system for C, a particular constraint S of the form s n # n s n Gamma1 # n Gamma1 : # 1 s 0 , where each # i is either = or , and fs n ; s 1 g is the set of all subterms of C. In ....

[Article contains additional citation context not shown here]

P. Narendran, M. Rusinowitch, and R. Verma. RPO constraint solving is in NP. In Annual Conference of the European Association of Computer Science Logic (CSL), Brno, Czech Republic, August 23--28, 1998. Abstract at http://www.dbai.tuwien.ac.at/CSL98.

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