Termination of String Rewriting with Matrix Interpretations

Hofbauer, Dieter; Waldmann, Johannes

doi:10.1007/11805618_25

Cited by 37 publications

(39 citation statements)

References 9 publications

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“…Finally, let us point another direction of extending WPO: unifying with the matrix interpretation method [13,8]. This goal is apparently challenging, since a matrix interpretation is not weakly simple in general.…”

Section: Discussionmentioning

confidence: 99%

Unifying the Knuth-Bendix, recursive path and polynomial orders

Yamada

Kusakari

Sakabe

2013

Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming

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We introduce a simplification order called the weighted path order (WPO). WPO compares weights of terms as in the Knuth-Bendix order (KBO), while WPO allows weights to be computed by an arbitrary interpretation which is weakly monotone and weakly simple. We investigate summations, polynomials and maximums for such interpretations. We show that KBO is a restricted case of WPO induced by summations, the polynomial order (POLO) is subsumed by WPO induced by polynomials, and the lexicographic path order (LPO) is a restricted case of WPO induced by maximums. By combining these interpretations, we obtain an instance of WPO that unifies KBO, LPO and POLO. We also present SMT encodings of our orders, as well as incorporating them in the dependency pair framework.

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Section: Discussionmentioning

confidence: 99%

Unifying the Knuth-Bendix, recursive path and polynomial orders

Yamada

Kusakari

Sakabe

2013

Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming

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“…Finally, it would be interesting to study whether our results can be extended to handle matrix interpretations [16,9], which have recently been adopted in automated tools as an alternative to RPO and polynomial interpretations for solving ordering constraints.…”

Section: Discussionmentioning

confidence: 99%

The recursive path and polynomial ordering for first-order and higher-order terms

Bofill¹,

Borralleras²,

Rodríguez-Carbonell

et al. 2012

Journal of Logic and Computation

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Abstract. In most termination tools two ingredients, namely recursive path orderings (RPO) and polynomial interpretation orderings (POLO), are used in a consecutive disjoint way to solve the final constraints generated from the termination problem. In this paper we present a simple ordering that combines both RPO and POLO and defines a family of orderings that includes both, and extend them with the possibility of having, at the same time, an RPO-like treatment for some symbols and a POLO-like treatment for the others. The ordering is extended to higher-order terms, providing a new fully automatable use of polynomial interpretations in combination with betareduction.

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“…Both [3] and [4] describe extremely fast SAT-based implementations. Successful SAT encodings of other termination techniques are described in [7,8,13,22,23].…”

Section: Introductionmentioning

confidence: 99%

Proving Termination Using Recursive Path Orders and SAT Solving

Schneider–Kamp

Thiemann

Annov

et al.

Frontiers of Combining Systems

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Abstract. We introduce a propositional encoding of the recursive path order with status (RPO). RPO is a combination of a multiset path order and a lexicographic path order which considers permutations of the arguments in the lexicographic comparison. Our encoding allows us to apply SAT solvers in order to determine whether a given term rewrite system is RPO-terminating. Furthermore, to apply RPO within the dependency pair framework, we combined our novel encoding for RPO with an existing encoding for argument filters. We implemented our contributions in the termination prover AProVE. Our experiments show that due to our encoding, combining termination provers with SAT solvers improves the performance of RPO-implementations by orders of magnitude.

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Termination of String Rewriting with Matrix Interpretations

Cited by 37 publications

References 9 publications

Unifying the Knuth-Bendix, recursive path and polynomial orders

Unifying the Knuth-Bendix, recursive path and polynomial orders

The recursive path and polynomial ordering for first-order and higher-order terms

Proving Termination Using Recursive Path Orders and SAT Solving

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