The complexity of testing ground reducibility for linear word rewriting systems with variables
Identifieur interne : 00C692 ( Main/Exploration ); précédent : 00C691; suivant : 00C693The complexity of testing ground reducibility for linear word rewriting systems with variables
Auteurs : Gregory Kucherov [France] ; Michaël Rusinowitch [France]Source :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: In [9] we proved that for a word rewriting system with variables $$x\mathcal{R}$$ and a word with variables Ω, it is undecidable if Ω is ground reducible by $$x\mathcal{R}$$ , that is if all the instances of Ω obtained by substituting its variables by non-empty words are reducible by $$x\mathcal{R}$$ . On the other hand, if $$x\mathcal{R}$$ is linear, the question is decidable for arbitrary (linear or non-linear) Ω. In this paper we futher study the complexity of the above problem and prove that it is co-NP-complete if both $$x\mathcal{R}$$ and Ω are restricted to be linear. The proof is based on the construction of a deterministic finite automaton for the language of words reducible by $$x\mathcal{R}$$ . The construction generalizes the well-known Aho-Corasick automaton for string matching against a set of keywords.
Url:
DOI: 10.1007/3-540-60381-6_16
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On the other hand, if $$x\mathcal{R}$$ is linear, the question is decidable for arbitrary (linear or non-linear) Ω. In this paper we futher study the complexity of the above problem and prove that it is co-NP-complete if both $$x\mathcal{R}$$ and Ω are restricted to be linear. The proof is based on the construction of a deterministic finite automaton for the language of words reducible by $$x\mathcal{R}$$ . The construction generalizes the well-known Aho-Corasick automaton for string matching against a set of keywords.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Vandœuvre-lès-Nancy</li></settlement></list><tree><country name="France"><region name="Grand Est"><name sortKey="Kucherov, Gregory" sort="Kucherov, Gregory" uniqKey="Kucherov G" first="Gregory" last="Kucherov">Gregory Kucherov</name></region><name sortKey="Kucherov, Gregory" sort="Kucherov, Gregory" uniqKey="Kucherov G" first="Gregory" last="Kucherov">Gregory Kucherov</name><name sortKey="Rusinowitch, Michael" sort="Rusinowitch, Michael" uniqKey="Rusinowitch M" first="Michaël" last="Rusinowitch">Michaël Rusinowitch</name><name sortKey="Rusinowitch, Michael" sort="Rusinowitch, Michael" uniqKey="Rusinowitch M" first="Michaël" last="Rusinowitch">Michaël Rusinowitch</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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