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Orienting rewrite rules with the KnuthBendix order
 Information and Computation
"... 2). We show that both the orientability problem is Pcomplete. Also we show that if a system is orientable using a realvalued instance of KBO, then it is also orientable using an integervalued instance of KBO. Therefore, all our results hold both for the integervalued and the realvalued KBO. 1 I ..."
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Cited by 13 (1 self)
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2). We show that both the orientability problem is Pcomplete. Also we show that if a system is orientable using a realvalued instance of KBO, then it is also orientable using an integervalued instance of KBO. Therefore, all our results hold both for the integervalued and the realvalued KBO. 1 Introduction In this section we give an informal overview of the results proved in this paper. The formal definitions will be given in the next section.
A decision procedure for the existential theory of term algebras with the KnuthBendix ordering
, 2000
"... We show the decidability of the existential theory of term algebras with any KnuthBendix ordering by giving a procedure for solving KnuthBendix ordering constraints. ..."
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Cited by 12 (4 self)
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We show the decidability of the existential theory of term algebras with any KnuthBendix ordering by giving a procedure for solving KnuthBendix ordering constraints.
Solved Forms for Path Ordering Constraints
 in `In Proc. 10th International Conference on Rewriting Techniques and Applications (RTA
, 1999
"... . A usual technique in symbolic constraint solving is to apply transformation rules until a solved form is reached for which the problem becomes simple. Ordering constraints are wellknown to be reducible to (a disjunction of) solved forms, but unfortunately no polynomial algorithm deciding the ..."
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. A usual technique in symbolic constraint solving is to apply transformation rules until a solved form is reached for which the problem becomes simple. Ordering constraints are wellknown to be reducible to (a disjunction of) solved forms, but unfortunately no polynomial algorithm deciding the satisfiability of these solved forms is known. Here we deal with a different notion of solved form, where fundamental properties of orderings like transitivity and monotonicity are taken into account. This leads to a new family of constraint solving algorithms for the full recursive path ordering with status (RPOS), and hence as well for other path orderings like LPO, MPO, KNS and RDO, and for all possible total precedences and signatures. Apart from simplicity and elegance from the theoretical point of view, the main contribution of these algorithms is on efficiency in practice. Since guessing is minimized, and, in particular, no linear orderings between the subterms are guessed, ...
KnuthBendix constraint solving is NPcomplete
 IN PROCEEDINGS OF 28TH INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING (ICALP), VOLUME 2076 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2000
"... We show that the problem of solving KnuthBendix ordering constraints is NPcomplete, as a corollary we show that the existential firstorder theory of any term algebra with the KnuthBendix ordering is NPcomplete. ..."
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Cited by 11 (3 self)
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We show that the problem of solving KnuthBendix ordering constraints is NPcomplete, as a corollary we show that the existential firstorder theory of any term algebra with the KnuthBendix ordering is NPcomplete.
On Ordering Constraints for Deduction with BuiltIn Abelian Semigroups, Monoids and Groups
 In: LICS, 16th IEEE Symposium on Logic in Computer Science, IEEE Computer
, 2001
"... . It is crucial for the performance of ordered resolution or paramodulationbased deduction systems that they incorporate specialized techniques to work efficiently with standard algebraic theories E. Essential ingredients for this purpose are term orderings that are Ecompatible, for the given E ..."
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Cited by 3 (2 self)
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. It is crucial for the performance of ordered resolution or paramodulationbased deduction systems that they incorporate specialized techniques to work efficiently with standard algebraic theories E. Essential ingredients for this purpose are term orderings that are Ecompatible, for the given E, and algorithms deciding constraint satisfiability for such orderings. Here we introduce a uniform technique providing the first such algorithms for some orderings for abelian semigroups, abelian monoids and abelian groups, which we believe will lead to reasonably efficient techniques for practice. The algorithms are optimal since we show that, for any wellfounded Ecompatible ordering for these E, the constraint satisfiability problem is NPhard even for conjunctions of inequations, and our algorithms are in NP. Keywords: symbolic constraints, term orderings, automated deduction. ? Both authors are partially supported by the ESPRIT Basic Research Action CCLII, ref. WG # 22457...
Practical Algorithms for Deciding Path Ordering Constraint Satisfaction
 Yale University/ Glasgow University
, 2001
"... this paper we introduce some new notions of solved form, where, in addition to the closure under the classical RPO decomposition rules, a restricted form of transitivity through variables is applied. It is proved that if C is a solved form in this sense, then it is satisfiable under extended signatu ..."
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Cited by 1 (0 self)
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this paper we introduce some new notions of solved form, where, in addition to the closure under the classical RPO decomposition rules, a restricted form of transitivity through variables is applied. It is proved that if C is a solved form in this sense, then it is satisfiable under extended signatures if, and only if, it has no cycle (Section 5)
Arithmetic Integration of Decision Procedures?
"... fficiency and increase the analysis accuracy. ..."
Constraint Solving for Term Orderings Compatible with Abelian Semigroups, Monoids and Groups
"... It is crucial for the performance of ordered resolution or paramodulationbased deduction systems that they incorporate specialized techniques to work efficiently with standard algebraic theories E. Essential ingredients for this purpose are term orderings that are Ecompatible, for the given E, and ..."
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It is crucial for the performance of ordered resolution or paramodulationbased deduction systems that they incorporate specialized techniques to work efficiently with standard algebraic theories E. Essential ingredients for this purpose are term orderings that are Ecompatible, for the given E, and algorithms deciding constraint satisfiability for such orderings.