Inf-datalog, modal logic and complexities

Foustoucos, Eugénie; Guessarian, Irène

doi:10.1051/ita:2007043

Foustoucos, Eugénie ; Guessarian, Irène

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 1, pp. 1-21.

Résumé

Inf-Datalog extends the usual least fixpoint semantics of Datalog with greatest fixpoint semantics: we defined inf-Datalog and characterized the expressive power of various fragments of inf-Datalog in [16]. In the present paper, we study the complexity of query evaluation on finite models for (various fragments of) inf-Datalog. We deduce a unified and elementary proof that global model-checking (i.e. computing all nodes satisfying a formula in a given structure) has 1. quadratic data complexity in time and linear program complexity in space for $C T L$ and alternation-free modal $μ$ -calculus, and 2. linear-space (data and program) complexities, linear-time program complexity and polynomial-time data complexity for $L μ_{k}$ (modal $μ$ -calculus with fixed alternation-depth at most $k$ ).

MR Zbl

DOI : 10.1051/ita:2007043

Classification : 68Q19, 03C13
Mots clés : databases, model-checking, specification languages, performance evaluation

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     title = {Inf-datalog, modal logic and complexities},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {1--21},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {1},
     year = {2009},
     doi = {10.1051/ita:2007043},
     mrnumber = {2483442},
     zbl = {1170.68015},
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     url = {http://archive.numdam.org/articles/10.1051/ita:2007043/}
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Foustoucos, Eugénie; Guessarian, Irène. Inf-datalog, modal logic and complexities. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 1, pp. 1-21. doi : 10.1051/ita:2007043. http://archive.numdam.org/articles/10.1051/ita:2007043/

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