H. Comon and R. Treinen. Ordering constraints on trees. In S. Tison, editor, Colloquium on Trees in Algebra and Programming, volume 787 of Lecture Notes in Computer Science, pages 1--14, Edinburgh, Scotland, 11-13 April 1994. Springer Verlag.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... 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 solved forms in [1] where for each i always s i or t i is a variable. In algorithms like the ones of [1] ....

Hubert Comon and Ralf Treinen. Ordering Constraints on Trees. In Proc. of Colloquium on Trees in Algebra and Programming (CAAP), LNCS 787, pages 1--14, Edinburgh, Scotland, April 1994. Springer-Verlag. 23

....due to its use of widening; in comparison, our analysis eciently nds the exact least xpoint by exploiting the structure of ane constraints, but only applies to a less general class of transfer functions. Our techniques also bear relation to earlier work on constraint solving in general [9 12, 28], especially that of solving set constraints [1 4,17,22 24,43] The class of tractable constraints we consider is closely related to de nite set constraints (set constraints of the form c(e 1 ; en ) X) 24] which always have a least solution. 9 Conclusions We have presented ecient ....

H. Comon and R. Treinen. Ordering constraints on trees. In S. Tison, editor, Colloquium on Trees in Algebra and Programming, volume 787 of Lecture Notes in Computer Science, pages 1-14, Edinburgh, Scotland, 11-13 April 1994. Springer Verlag.

.... 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 , called solved forms in [Com90] where for each i always s i or t i is a variable. In algorithms like the ones of ....

Hubert Comon and Ralf Treinen. Ordering Constraints on Trees. In Proc. of Colloquium on Trees in Algebra and Programming (CAAP), LNCS 787, pages 1--14, Edinburgh, Scotland, April 1994. Springer-Verlag.

....the case where the symbolic constraints under consideration are based on an ordering predicate interpreted as a recursive path ordering on terms. We are giving only the basic results and references on the literature as well as more detailed account of results could be found in the survey paper [CT94] As this will be detailed in other lectures of this school, this kind of ordering constraints is extremely useful in theorem proving [HR91, BGLS95] as well as in programming language design since they allow to keep into account simpli cation as well as deletion strategies. This section is ....

Hubert Comon and Ralf Treinen. Ordering constraints on trees. In Sophie Tison, editor, Colloquium on Trees in Algebra and Programming, volume 787 of Lecture Notes in Computer Science, pages 1-14, Edinburgh, Scotland, April 1994. Springer Verlag.

.... 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 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 solved forms, where for each i always at least one of s i or t i is a variable. Solved forms are obtained by ....

Comon H. and Treinen R. [1994], Ordering Constraints on Trees, in `Proc. of Colloquium on Trees in Algebra and Programming (CAAP)', LNCS 787, Springer-Verlag, Edinburgh, Scotland, pp. 1--14.

....more taken on by algorithms that decide solvability of the unification problems. In this setting, more general constraints than the equational constraints s = t of unification problems become important as well. For example, one might be interested in ordering constraints of the form s t on terms [CT94], where the predicate could be interpreted as the subterm ordering or as a reduction ordering. For unification, the problem of combining decision procedures has been solved in [BS92] in a rather general way. The main tool of this combination method is a decomposition algorithm, which separates a ....

....subterm ordering. For our combination result to apply, however, the positive theory of these structures must be decidable. For a total lexicographic path ordering, this is not the case. For the subterm ordering, the existential theory is decidable, but the full first order theory is undecidable [CT94]. Decidability of the positive theory is still an open problem. For partial lexicographic path orderings, even decidability of the existential theory is unknown. Combination of constraint solving techniques in the presence of predicate symbols other than equality have independently been ....

H. Comon and R. Treinen. Ordering constraints on trees. In Colloquium on Trees in Algebra and Programming (CAAP), LNCS, 1994.

.... 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 solved forms in [Com90] where for each i always s i or t i is a variable. In algorithms like the ones of ....

Hubert Comon and Ralf Treinen. Ordering Constraints on Trees. In Proc. CAAP, LNCS 787, Edinburgh, Scotland, Springer-Verlag.

....more taken on by algorithms that decide solvability of the unification problems. In this setting, more general constraints than the equational constraints s = t of unification problems become important as well. For example, one might be interested in ordering constraints of the form s t on terms [CT94], where the predicate could be interpreted as the subterm ordering or as a reduction ordering (such as the recursive path ordering) If more than one special inference method is to be integrated into a general purpose deductive system then one must combine these special methods. In order to ....

....to apply, however, the positive theory of these structures must be decidable. For a total lexicographic path ordering, this is not the case. For the subterm ordering and for partial lexicographic path orderings, the existential theory is decidable, but the full first order theory is undecidable [CT94]. Decidability of the positive theory is still an open problem. Combination of constraint solving techniques in the presence of predicate symbols other than equality have independently been considered by H. Kirchner and Ch. Ringeissen [KR94] However, their approach is based on the rewriting and ....

H. Comon and R. Treinen. Ordering constraints on trees. In Colloquium on trees in Algebra and Programming (CAAP), Lecture Notes in Computer Science, Edinburgh, Scotland, 1994. Springer Verlag.

....more taken on by algorithms that decide solvability of the unification problems. In this setting, more general constraints than the equational constraints s = t of unification problems become important as well. For example, one might be interested in ordering constraints of the form s t on terms [CT94], where the predicate could be interpreted as the subterm ordering or as a reduction ordering. For unification, the problem of combining decision procedures has been solved in [BS92] in a rather general way. The main tool of this combination method is a decomposition algorithm, which separates a ....

....to apply, however, the positive theory of these structures must be decidable. For a total lexicographic path ordering, this is not the case. For the subterm ordering and for partial lexicographic path orderings, the existential theory is decidable, but the full first order theory is undecidable [CT94]. Decidability of the positive theory is still an open problem. Combination of constraint solving techniques in the presence of predicate symbols other than equality have independently been considered by H. Kirchner and Ch. Ringeissen [KR94] However, their approach is based on the rewriting and ....

H. Comon and R. Treinen. Ordering constraints on trees. In Colloquium on Trees in Algebra and Programming (CAAP), LNCS, 1994.

.... in which each variable in goal terms is associated with a regular tree language from which a term to substitute for the variable is chosen; disunification problems[3] in which some variables in goal terms must be substituted by different terms; unification problems with ordering constraints [4] in which terms to substitute for variables must satisfy given term ordering. SUPCS and TDunification problems can be regarded as two of such extensions of unification problems. Since those problems are highly related with each other, our results can be translated into those other extensions ....

H. Comon and R. Treinen, "Ordering constraints on trees," Proc. of the Nineteenth Colloquium on Trees in Algebra and Programming, LNCS 787, pp.1--14, Springer-Verlag, Berlin, 1994.

.... 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 , called solved forms in [Com90] where for each i always s i or t i is a variable. In algorithms like the ones of ....

Hubert Comon and Ralf Treinen. Ordering Constraints on Trees. In Proc. of Colloquium on Trees in Algebra and Programming (CAAP), LNCS, Edinburgh, Scotland, April 1994. Springer-Verlag.

....in first order theorem proving involving This work is partly supported by the GDR Programmation du CNRS , the ESPRIT Working Group CCL and the ESPRIT Basic Research Action TYPES . AC operators [28,29] Solving ordering constraints is also known to be easier when using total orderings [6, 13], hence having simply defined total AC orderings is certainly a good basis for use in AC ordering constraints. Defining a total AC compatible reduction ordering was a very difficult problem and has been solved only very recently (in 1991) by Narendran and Rusinowitch [24] Unfortunately their ....

H. Comon and R. Treinen. Ordering constraints on trees. In S. Tison, editor, Proc. CAAP 94, LNCS, Edinburgh, Apr. 1994. Springer Verlag. (Invited Lecture).

....point of view replacing one constraint set with an equivalent one does not change the observable behavior of the constraint system. A similar notion is used in [33] for simplifying subtyping constraints. There is also related work in term rewriting and constraint solving over trees in general [8, 10]. The work in this paper is inspired by work in this area. Maher shows the first order theory of finite trees, infinite trees, and rational trees is decidable by giving a complete axiomatization [21] Many researchers consider various order relations among trees, similar to the subtype orders. ....

H. Comon and R. Treinen. Ordering constraints on trees. In S. Tison, editor, Colloquium on Trees in Algebra and Programming, volume 787 of Lecture Notes in Computer Science, pages 1--14, Edinburgh, Scotland, 11-13 April 1994. Springer Verlag.

....point of view replacing one constraint set with an equivalent one does not change the observable behavior of the constraint system. A similar notion is used in [34] for simplifying subtyping constraints. There is also related work in term rewriting and constraint solving over trees in general [8, 9, 11]. The work in this paper is inspired by work in this area. Maher shows the rst order theory of nite trees, in nite trees, and rational trees is decidable by giving a complete axiomatization [22] Many researchers consider various order relations among trees, similar to the subtype orders. ....

H. Comon and R. Treinen. Ordering constraints on trees. In S. Tison, editor, Colloquium on Trees in Algebra and Programming, volume 787 of Lecture Notes in Computer Science, pages 1-14, Edinburgh, Scotland, 11-13 April 1994. Springer Verlag.

....structures. 2.3. Some other constraint systems There are other important predicates in practice. Term orderings, for example, surface naturally in mechanizing deduction since they allow reducing the search space by eliminating those inferences which do not satisfy certain ordering conditions (see [9, 31, 41, 12] among others for term ordering constraint solving) Membership predicates are important in typed languages where they are interpreted as set membership (see e.g. 10] for constraint solving) Set predicates have been used for defining and computing partial interpretations of logic programs (see ....

Hubert Comon and Ralf Treinen. Ordering constraints on trees. In Sophie Tison, editor, Colloquium on Trees in Algebra and Programming, volume 787 of Lecture Notes in Computer Science, pages 1--14, Edinburgh, Scotland, 1994. Springer-Verlag. (Invited Lecture).

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