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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Vydáno v:Discrete mathematics and theoretical computer science Ročník DMTCS Proceedings vol. AQ,...; číslo Proceedings; s. 303 - 322
Hlavní autoři: Jacquet, Philippe, Szpankowski, Wojciech
Médium: Journal Article Konferenční příspěvek
Jazyk:angličtina
Vydáno: DMTCS 01.01.2012
Discrete Mathematics and Theoretical Computer Science
Discrete Mathematics & Theoretical Computer Science
Edice:DMTCS Proceedings
Témata:
[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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Popis
Shrnutí: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.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.3001