Joint String Complexity for Markov Sources

String complexity is defined as the cardinality of a set of all distinct words (factors) of a given string. For two strings, we define $\textit{joint string complexity}$ as the set of words that are common to both strings. We also relax this definition and introduce $\textit{joint semi-complexity}$...

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Published in:Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings vol. AQ,...; no. Proceedings; pp. 303 - 322
Main Authors: Jacquet, Philippe, Szpankowski, Wojciech
Format: Journal Article Conference Proceeding
Language:English
Published: DMTCS 01.01.2012
Discrete Mathematics and Theoretical Computer Science
Discrete Mathematics & Theoretical Computer Science
Series:DMTCS Proceedings
Subjects:
[info.info-cg] computer science [cs]/computational geometry [cs.cg]
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
[info.info-ds] computer science [cs]/data structures and algorithms [cs.ds]
[math.math-co] mathematics [math]/combinatorics [math.co]
Combinatorics
Computational Geometry
Computer Science
Data Structures and Algorithms
Discrete Mathematics
double depoissonization
double mellin transform
Mathematics
saddle point method
semi-complexity
string complexity
double Mellin transform
String complexity
saddle point method
semi-complexity
double depoissonization
ISSN:1365-8050, 1462-7264, 1365-8050
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Abstract String complexity is defined as the cardinality of a set of all distinct words (factors) of a given string. For two strings, we define $\textit{joint string complexity}$ as the set of words that are common to both strings. We also relax this definition and introduce $\textit{joint semi-complexity}$ restricted to the common words appearing at least twice in both strings. String complexity finds a number of applications from capturing the richness of a language to finding similarities between two genome sequences. In this paper we analyze joint complexity and joint semi-complexity when both strings are generated by a Markov source. The problem turns out to be quite challenging requiring subtle singularity analysis and saddle point method over infinity many saddle points leading to novel oscillatory phenomena with single and double periodicities.
AbstractList String complexity is defined as the cardinality of a set of all distinct words (factors) of a given string. For two strings, we define $\textit{joint string complexity}$ as the set of words that are common to both strings. We also relax this definition and introduce $\textit{joint semi-complexity}$ restricted to the common words appearing at least twice in both strings. String complexity finds a number of applications from capturing the richness of a language to finding similarities between two genome sequences. In this paper we analyze joint complexity and joint semi-complexity when both strings are generated by a Markov source. The problem turns out to be quite challenging requiring subtle singularity analysis and saddle point method over infinity many saddle points leading to novel oscillatory phenomena with single and double periodicities.
Author Jacquet, Philippe
Szpankowski, Wojciech
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  givenname: Philippe
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  fullname: Jacquet, Philippe
  organization: Alcatel-Lucent Bell Labs France [Nozay]
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  givenname: Wojciech
  surname: Szpankowski
  fullname: Szpankowski, Wojciech
  organization: Department of Computer Science [Purdue]
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Keywords double Mellin transform
String complexity
saddle point method
semi-complexity
double depoissonization
Language English
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Snippet String complexity is defined as the cardinality of a set of all distinct words (factors) of a given string. For two strings, we define $\textit{joint string...
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SubjectTerms [info.info-cg] computer science [cs]/computational geometry [cs.cg]
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
[info.info-ds] computer science [cs]/data structures and algorithms [cs.ds]
[math.math-co] mathematics [math]/combinatorics [math.co]
Combinatorics
Computational Geometry
Computer Science
Data Structures and Algorithms
Discrete Mathematics
double depoissonization
double mellin transform
Mathematics
saddle point method
semi-complexity
string complexity
Title Joint String Complexity for Markov Sources
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