On the relation between Context and Sequence Unification

Kutsia, Temur; Levy, Jordi; Villaret, Mateu

doi:10.1016/j.jsc.2009.07.001

Cited by 5 publications

(2 citation statements)

References 34 publications

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“…To show decidability, we define a translation from REOSU problems into word equations with regular constraints. The idea is similar to the one of Levy and Villaret (2001) , used to translate context equations into traversal equations, or of Kutsia et al (2007, 2010) , used to translate left-hole context equations into word equations with regular constraints.…”

Section: Decidability Of Reosumentioning

confidence: 99%

Regular expression order-sorted unification and matching

Kutsia

Marin

2015

Journal of Symbolic Computation

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We extend order-sorted unification by permitting regular expression sorts for variables and in the domains of function symbols. The obtained signature corresponds to a finite bottom-up unranked tree automaton. We prove that regular expression order-sorted (REOS) unification is of type infinitary and decidable. The unification problem presented by us generalizes some known problems, such as, e.g., order-sorted unification for ranked terms, sequence unification, and word unification with regular constraints. Decidability of REOS unification implies that sequence unification with regular hedge language constraints is decidable, generalizing the decidability result of word unification with regular constraints to terms. A sort weakening algorithm helps to construct a minimal complete set of REOS unifiers from the solutions of sequence unification problems. Moreover, we design a complete algorithm for REOS matching, and show that this problem is NP-complete and the corresponding counting problem is #P-complete.

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Section: Decidability Of Reosumentioning

confidence: 99%

Regular expression order-sorted unification and matching

Kutsia

Marin

2015

Journal of Symbolic Computation

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“…(For instance, 5 ) it computes 11,685 generalizations, most of them several times, until it selects a single one, e.g., f (x 1 , x 2 , x 3 , x 4 , x 5 ), on the minimization step.) The minimization step involves NP-complete hedge matching algorithm (see [20,25]) performed on the pairs of elements of the generalization set. Hence, this algorithm is only of theoretical interest and falls short of being practically useful.…”

Section: Example 311 For the Termsmentioning

confidence: 99%

Anti-unification for Unranked Terms and Hedges

2013

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We study anti-unification for unranked terms and hedges that may contain term and hedge variables. The anti-unification problem of two hedgess 1 ands 2 is concerned with finding their generalization, a hedgeq such that boths 1 ands 2 are instances ofq under some substitutions. Hedge variables help to fill in gaps in generalizations, while term variables abstract single (sub)terms with different top function symbols. First, we design a complete and minimal algorithm to compute least general generalizations. Then, we improve the efficiency of the algorithm by restricting possible alternatives permitted in the generalizations. The restrictions are imposed with the help of a rigidity function, which is a parameter in the improved algorithm and selects certain common subsequences from the hedges to be generalized. The obtained rigid anti-unif ication algorithm is further made more precise by permitting combination of hedge and term variables in generalizations. Finally, we indicate a possible application of the algorithm in software engineering.

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