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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Bibliographic Details
Published in:Theory of computing systems Vol. 59; no. 1; pp. 24 - 51
Main Authors: Fernau, Henning, Schmid, Markus L., Villanger, Yngve
Format: Journal Article
Language:English
Published: New York Springer US 01.07.2016
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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 .
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ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-015-9635-3