<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1405-5546</journal-id>
<journal-title><![CDATA[Computación y Sistemas]]></journal-title>
<abbrev-journal-title><![CDATA[Comp. y Sist.]]></abbrev-journal-title>
<issn>1405-5546</issn>
<publisher>
<publisher-name><![CDATA[Instituto Politécnico Nacional, Centro de Investigación en Computación]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1405-55462020000100281</article-id>
<article-id pub-id-type="doi">10.13053/cys-24-1-2940</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Presburger Constraints in Trees]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Bárcenas]]></surname>
<given-names><![CDATA[Everardo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Benítez-Guerrero]]></surname>
<given-names><![CDATA[Edgard]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Lavalle]]></surname>
<given-names><![CDATA[Jesús]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Molero-Castillo]]></surname>
<given-names><![CDATA[Guillermo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional Autónoma de México  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Veracruzana  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Benemérita Universidad Autónoma de Puebla  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>03</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>03</month>
<year>2020</year>
</pub-date>
<volume>24</volume>
<numero>1</numero>
<fpage>281</fpage>
<lpage>303</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1405-55462020000100281&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1405-55462020000100281&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1405-55462020000100281&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract The fully enriched &#956;-calculus is an expressive propositional modal logic with least and greatest fixed-points, nominals, inverse programs and graded modalities. Several fragments of this logic are known to be decidable in EXPTIME. However, the full logic is undecidable. Nevertheless, it has been recently shown that the fully enriched &#956;-calculus is decidable in EXPTIME when its models are finite trees. In the present work, we study the fully-enriched &#956;-calculus for trees extended with Presburger constraints. These constraints generalize graded modalities by restricting the number of children nodes with respect to Presburger arithmetic expressions. We show that this extension is decidable in EXPTIME. In addition, we also identify decidable extensions of regular tree languages (XML schemas) with interleaving and counting operators. This is achieved by a linear characterization in terms of the logic. Regular path queries (XPath) with Presburger constraints on children paths are also characterized. These results imply new optimal reasoning (emptiness, containment, equivalence) bounds on counting extensions of XPath queries and XML schemas.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Presburger arithmetic]]></kwd>
<kwd lng="en"><![CDATA[modal logics]]></kwd>
<kwd lng="en"><![CDATA[automated reasoning]]></kwd>
<kwd lng="en"><![CDATA[XPath]]></kwd>
<kwd lng="en"><![CDATA[regular languages]]></kwd>
<kwd lng="en"><![CDATA[interleaving]]></kwd>
</kwd-group>
</article-meta>
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