On the Parameterised Complexity of String Morphism Problems

Given a source string u and a target string w , to decide whether w can be obtained by applying a string morphism on u (i. e., uniformly replacing the symbols in u by strings) constitutes an 𝓝 𝓟 -complete problem. We present a multivariate analysis of this problem (and its many variants) from the vi...

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Vydáno v:	Theory of computing systems Ročník 59; číslo 1; s. 24 - 51
Hlavní autoři:	Fernau, Henning, Schmid, Markus L., Villanger, Yngve
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.07.2016 Springer Nature B.V
Témata:	Complexity theory Computation Computer Science Hardness Mathematical analysis Multivariate analysis Pinning Strings Studies Symbols Texts Theory of Computation String problems String morphisms Exponential time hypothesis Parameterised complexity Pattern languages
ISSN:	1432-4350, 1433-0490
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Abstract	Given a source string u and a target string w , to decide whether w can be obtained by applying a string morphism on u (i. e., uniformly replacing the symbols in u by strings) constitutes an 𝓝 𝓟 -complete problem. We present a multivariate analysis of this problem (and its many variants) from the viewpoint of parameterised complexity theory, thereby pinning down the sources of its computational hardness. Our results show that most parameterised variants of the string morphism problem are fixed-parameter intractable and, apart from some very special cases, tractable variants can only be obtained by considering a large part of the input as parameters, namely the length of w and the number of different symbols in u .
AbstractList	(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image).Given a source string u and a target string w, to decide whether w can be obtained by applying a string morphism on u (i. e., uniformly replacing the symbols in u by strings) constitutes an ...-complete problem. We present a multivariate analysis of this problem (and its many variants) from the viewpoint of parameterised complexity theory, thereby pinning down the sources of its computational hardness. Our results show that most parameterised variants of the string morphism problem are fixed-parameter intractable and, apart from some very special cases, tractable variants can only be obtained by considering a large part of the input as parameters, namely the length of w and the number of different symbols in u. Given a source string u and a target string w , to decide whether w can be obtained by applying a string morphism on u (i. e., uniformly replacing the symbols in u by strings) constitutes an 𝓝 𝓟 -complete problem. We present a multivariate analysis of this problem (and its many variants) from the viewpoint of parameterised complexity theory, thereby pinning down the sources of its computational hardness. Our results show that most parameterised variants of the string morphism problem are fixed-parameter intractable and, apart from some very special cases, tractable variants can only be obtained by considering a large part of the input as parameters, namely the length of w and the number of different symbols in u .
Author	Fernau, Henning Schmid, Markus L. Villanger, Yngve
Author_xml	– sequence: 1 givenname: Henning surname: Fernau fullname: Fernau, Henning organization: Fachbereich IV – Abteilung Informatikwissenschaften, Universität Trier – sequence: 2 givenname: Markus L. surname: Schmid fullname: Schmid, Markus L. email: MSchmid@uni-trier.de organization: Fachbereich IV – Abteilung Informatikwissenschaften, Universität Trier – sequence: 3 givenname: Yngve surname: Villanger fullname: Villanger, Yngve organization: Department of Informatics, University of Bergen
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Cites_doi	10.1016/0020-0190(79)90135-2 10.1016/0167-8655(94)00091-G 10.1016/j.tcs.2008.09.065 10.1016/j.tcs.2006.07.016 10.1006/jcss.2001.1774 10.1142/S0129054106004017 10.1080/00207169408804252 10.1016/j.disopt.2010.10.003 10.1016/j.jda.2006.10.001 10.1016/S0022-0000(03)00073-4 10.1006/jcss.1996.0003 10.1142/S012905410300214X 10.1007/978-3-642-33122-0_12 10.1145/800135.804406 10.1016/S0022-0000(03)00078-3 10.1007/3-540-45061-0_72 10.1007/978-3-642-28332-1_40 10.1007/978-3-642-18098-9_26 10.1051/ita/1994283-402331 10.1007/978-3-642-24412-4_10 10.1007/978-1-4471-2155-8_35 10.1007/978-3-642-16533-7 10.1007/3-540-58140-5_10 10.1007/978-3-642-59136-5_7 10.1007/978-1-4612-0515-9 10.1007/978-3-642-38905-4_10 10.1007/978-3-642-03784-9_29
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Snippet	Given a source string u and a target string w , to decide whether w can be obtained by applying a string morphism on u (i. e., uniformly replacing the symbols... (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) Given a source string u and a target string w, to decide whether w can be obtained... (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image).Given a source string u and a target string w, to decide whether w can be obtained...
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SubjectTerms	Complexity theory Computation Computer Science Hardness Mathematical analysis Multivariate analysis Pinning Strings Studies Symbols Texts Theory of Computation
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Title	On the Parameterised Complexity of String Morphism Problems
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