Finite Automata Intersection Non-Emptiness: Parameterized Complexity Revisited
The problem DFA-Intersection-Nonemptiness asks if a given number of deterministic automata accept a common word. In general, this problem is PSPACE-complete. Here, we investigate this problem for the subclasses of commutative automata and automata recognizing sparse languages. We show that in both c...
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| creator | Fernau, Henning Hoffmann, Stefan Wehar, Michael |
| description | The problem DFA-Intersection-Nonemptiness asks if a given number of
deterministic automata accept a common word. In general, this problem is
PSPACE-complete. Here, we investigate this problem for the subclasses of
commutative automata and automata recognizing sparse languages. We show that in
both cases DFA-Intersection-Nonemptiness is complete for NP and for the
parameterized class $W[1]$, where the number of input automata is the
parameter, when the alphabet is fixed. Additionally, we establish the same
result for Tables Non-Empty Join, a problem that asks if the join of several
tables (possibly containing null values) in a database is non-empty. Lastly, we
show that Bounded NFA-Intersection-Nonemptiness, parameterized by the length
bound, is $\mbox{co-}W[2]$-hard with a variable input alphabet and for
nondeterministic automata recognizing finite strictly bounded languages,
yielding a variant leaving the realm of $W[1]$. |
| doi_str_mv | 10.48550/arxiv.2108.05244 |
| format | Article |
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deterministic automata accept a common word. In general, this problem is
PSPACE-complete. Here, we investigate this problem for the subclasses of
commutative automata and automata recognizing sparse languages. We show that in
both cases DFA-Intersection-Nonemptiness is complete for NP and for the
parameterized class $W[1]$, where the number of input automata is the
parameter, when the alphabet is fixed. Additionally, we establish the same
result for Tables Non-Empty Join, a problem that asks if the join of several
tables (possibly containing null values) in a database is non-empty. Lastly, we
show that Bounded NFA-Intersection-Nonemptiness, parameterized by the length
bound, is $\mbox{co-}W[2]$-hard with a variable input alphabet and for
nondeterministic automata recognizing finite strictly bounded languages,
yielding a variant leaving the realm of $W[1]$.</description><identifier>DOI: 10.48550/arxiv.2108.05244</identifier><language>eng</language><subject>Computer Science - Computational Complexity ; Computer Science - Databases ; Computer Science - Formal Languages and Automata Theory</subject><creationdate>2021-08</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2108.05244$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2108.05244$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Fernau, Henning</creatorcontrib><creatorcontrib>Hoffmann, Stefan</creatorcontrib><creatorcontrib>Wehar, Michael</creatorcontrib><title>Finite Automata Intersection Non-Emptiness: Parameterized Complexity Revisited</title><description>The problem DFA-Intersection-Nonemptiness asks if a given number of
deterministic automata accept a common word. In general, this problem is
PSPACE-complete. Here, we investigate this problem for the subclasses of
commutative automata and automata recognizing sparse languages. We show that in
both cases DFA-Intersection-Nonemptiness is complete for NP and for the
parameterized class $W[1]$, where the number of input automata is the
parameter, when the alphabet is fixed. Additionally, we establish the same
result for Tables Non-Empty Join, a problem that asks if the join of several
tables (possibly containing null values) in a database is non-empty. Lastly, we
show that Bounded NFA-Intersection-Nonemptiness, parameterized by the length
bound, is $\mbox{co-}W[2]$-hard with a variable input alphabet and for
nondeterministic automata recognizing finite strictly bounded languages,
yielding a variant leaving the realm of $W[1]$.</description><subject>Computer Science - Computational Complexity</subject><subject>Computer Science - Databases</subject><subject>Computer Science - Formal Languages and Automata Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz0FrwyAYxnEvO4xuH2Cn-QWSadSou5XQboXSjtF7UPMKQk2CutLu06_rdnoOD_zhh9ATJTVXQpAXk87hVDeUqJqIhvN7tFuHMRTAy68yRVMM3owFUgZXwjTi3TRWqziXMELOr_jDJBPh-odvGHA3xfkI51Au-BNOIV8zwwO68-aY4fF_F-iwXh2692q7f9t0y21lWskrprmT1A1OC6YtUO400arVSjprLXgviZXgiW0c9bpVjGrOQEiupeRisGyBnv-yN1A_pxBNuvS_sP4GYz8YQEmM</recordid><startdate>20210811</startdate><enddate>20210811</enddate><creator>Fernau, Henning</creator><creator>Hoffmann, Stefan</creator><creator>Wehar, Michael</creator><scope>AKY</scope><scope>GOX</scope></search><sort><creationdate>20210811</creationdate><title>Finite Automata Intersection Non-Emptiness: Parameterized Complexity Revisited</title><author>Fernau, Henning ; Hoffmann, Stefan ; Wehar, Michael</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a674-394c71cdc9539be14c90986987cbbbeff70b7ef0b2c1f96831943e57497745db3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Computer Science - Computational Complexity</topic><topic>Computer Science - Databases</topic><topic>Computer Science - Formal Languages and Automata Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Fernau, Henning</creatorcontrib><creatorcontrib>Hoffmann, Stefan</creatorcontrib><creatorcontrib>Wehar, Michael</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Fernau, Henning</au><au>Hoffmann, Stefan</au><au>Wehar, Michael</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Finite Automata Intersection Non-Emptiness: Parameterized Complexity Revisited</atitle><date>2021-08-11</date><risdate>2021</risdate><abstract>The problem DFA-Intersection-Nonemptiness asks if a given number of
deterministic automata accept a common word. In general, this problem is
PSPACE-complete. Here, we investigate this problem for the subclasses of
commutative automata and automata recognizing sparse languages. We show that in
both cases DFA-Intersection-Nonemptiness is complete for NP and for the
parameterized class $W[1]$, where the number of input automata is the
parameter, when the alphabet is fixed. Additionally, we establish the same
result for Tables Non-Empty Join, a problem that asks if the join of several
tables (possibly containing null values) in a database is non-empty. Lastly, we
show that Bounded NFA-Intersection-Nonemptiness, parameterized by the length
bound, is $\mbox{co-}W[2]$-hard with a variable input alphabet and for
nondeterministic automata recognizing finite strictly bounded languages,
yielding a variant leaving the realm of $W[1]$.</abstract><doi>10.48550/arxiv.2108.05244</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Computational Complexity Computer Science - Databases Computer Science - Formal Languages and Automata Theory |
| title | Finite Automata Intersection Non-Emptiness: Parameterized Complexity Revisited |
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