On Positive TAGED with a Bounded Number of Constraints
Identifieur interne : 001A18 ( Main/Exploration ); précédent : 001A17; suivant : 001A19On Positive TAGED with a Bounded Number of Constraints
Auteurs : Pierre-Cyrille Heam [France] ; Vincent Hugot [France] ; Olga Kouchnarenko [France]Source :
Abstract
Tree Automata With Global Equality Constraints (aka. positive TAGED, or TAGE) are a variety of Bottom-Up Tree Automata, with added expressive power. While there is interest in using this formalism to extend existing regular model-checking frameworks -- built on vanilla tree automata -- such a project can only be practical if the algorithmic complexity of common decision problems is kept tractable. Unfortunately, useful TAGE decision problems sport very high complexities: Membership is NP-complete, Emptiness and Finiteness are both EXPTIME-complete, Universality and Inclusion are undecidable. It is well-known that restricting the kind of equality constraints can have a dramatic effect on complexity, as evidenced by Rigid Tree Automata. However, the influence of the number of constraints on complexity has yet to be examined. In this paper, we focus on three common decision problems: Emptiness, Finiteness and Membership, and study their algorithmic complexity under a bounded number of equality constraints.
Url:
DOI: 10.1007/978-3-642-31606-7_29
Affiliations:
- France
- Franche-Comté
- Belfort, Besançon
- Université de Bourgogne Franche-Comté, Université de Franche-Comté, Université de technologie de Belfort-Montbéliard
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Le document en format XML
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<front><div type="abstract" xml:lang="en">Tree Automata With Global Equality Constraints (aka. positive TAGED, or TAGE) are a variety of Bottom-Up Tree Automata, with added expressive power. While there is interest in using this formalism to extend existing regular model-checking frameworks -- built on vanilla tree automata -- such a project can only be practical if the algorithmic complexity of common decision problems is kept tractable. Unfortunately, useful TAGE decision problems sport very high complexities: Membership is NP-complete, Emptiness and Finiteness are both EXPTIME-complete, Universality and Inclusion are undecidable. It is well-known that restricting the kind of equality constraints can have a dramatic effect on complexity, as evidenced by Rigid Tree Automata. However, the influence of the number of constraints on complexity has yet to be examined. In this paper, we focus on three common decision problems: Emptiness, Finiteness and Membership, and study their algorithmic complexity under a bounded number of equality constraints.</div>
</front>
</TEI>
<affiliations><list><country><li>France</li>
</country>
<region><li>Franche-Comté</li>
</region>
<settlement><li>Belfort</li>
<li>Besançon</li>
</settlement>
<orgName><li>Université de Bourgogne Franche-Comté</li>
<li>Université de Franche-Comté</li>
<li>Université de technologie de Belfort-Montbéliard</li>
</orgName>
</list>
<tree><country name="France"><region name="Franche-Comté"><name sortKey="Heam, Pierre Cyrille" sort="Heam, Pierre Cyrille" uniqKey="Heam P" first="Pierre-Cyrille" last="Heam">Pierre-Cyrille Heam</name>
</region>
<name sortKey="Hugot, Vincent" sort="Hugot, Vincent" uniqKey="Hugot V" first="Vincent" last="Hugot">Vincent Hugot</name>
<name sortKey="Kouchnarenko, Olga" sort="Kouchnarenko, Olga" uniqKey="Kouchnarenko O" first="Olga" last="Kouchnarenko">Olga Kouchnarenko</name>
</country>
</tree>
</affiliations>
</record>
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