Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-20T02:56:43.901Z Has data issue: false hasContentIssue false
  • English
  • Français

Inf-datalog, Modal Logic and Complexities

Published online by Cambridge University Press:  20 December 2007

Eugénie Foustoucos  and
Irène Guessarian
Eugénie Foustoucos
Affiliation:
MPLA, National and Capodistrian University of Athens, Department of Mathematics, Panepistimiopolis, 15784 Athens, Greece; aflaw@otenet.gr
Irène Guessarian
Affiliation:
LIAFA, UMR 7089, Université Paris 7, case 7014, 2 Place Jussieu, 75251 Paris Cedex 5, France; ig@liafa.jussieu.fr
Get access

Abstract

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 [CITE]. 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 CTL and alternation-free modal μ-calculus, and 2. linear-space (data and program) complexities, linear-time program complexity and polynomial-time data complexity for Lµk (modal μ-calculus with fixed alternation-depth at most k).

Keywords

Databasesmodel-checkingspecification languagesperformance evaluation.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 43 , Issue 1 , January 2009 , pp. 1 - 21
Copyright
© EDP Sciences, 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

S. Abiteboul, R. Hull and V. Vianu, Foundations of databases. Addison-Wesley (1995).
Arnold, A. and Crubillé, P., A linear algorithm to solve fixed-point equations on transition systems. Inform. Process. Lett. 29 (1988) 57–66. CrossRef
A. Arnold and D. Niwiński, Rudiments of µ-calculus. Stud. Logic Found. Math. 146, Elsevier Science, North-Holland, Amsterdam (2001).
Bradfield, J., Fixpoint alternation: Arithmetic, transition systems, and the binary tree. RAIRO-Theor. Inf. Appl. 33 (1999) 341–356. CrossRef
Browne, A., Clarke, E., Jha, S., Long, D. and Marrero, W., An improved algorithm for the evaluation of fixpoint expressions. Theor. Comput. Sci. 178 (1997) 237–255. CrossRef
W. Charatonik, D. McAllester, D. Niwínski, A. Podelski and I. Walukiewicz, The horn Mu-calculus. LICS (1998) 58–69.
Clarke, E.M., Emerson, E.A. and Sistla, A.P., Automatic Verification of finite-state concurrent systems using temporal logic specifications. ACM TOPLAS 8 (1986) 244–263. CrossRef
Cleaveland, R. and Steffan, B., A linear time model-checking algorithm for the alternation-free modal mu-calculus. Formal Method. Syst. Des. 2 (1993) 121–148. CrossRef
E. Emerson, Temporal and modal logic. Handbook of Theoretical Computer Science (1990) 997–1072.
E. Emerson, Model-Checking and the Mu-Calculus, in Descriptive Complexity and Finite Models, edited by N. Immerman and Ph. Kolaitis, American Mathematical Society (1997).
E.A. Emerson and C.L. Lei, Efficient model-checking in fragments of the propositional µ-calculus, in Proc. of 1rst Symposium on Logic in Computer Science (1986) 267–278.
E. Foustoucos and I. Guessarian, Complexity of Monadic inf-datalog. Application to temporal logic. Extended abstract in Proceedings 4th Panhellenic Logic Symposium (2003) 95–99.
G. Gottlob and C. Koch, Monadic Datalog and the expressive power of web information extraction languages. Proc. PODS'02 (2002) 17–28.
Gottlob, G., Grädel, E. and Veith, H., Datalog LITE: temporal versus deductive reasoning in verification. ACM T. Comput. Log. 3 (2002) 39–74.
Griffault, A. and Vincent, A., The Mec 5 model-checker, CAV'04. Lect. Notes Comput. Sci. 3114 (2004) 488–491. CrossRef
Guessarian, I., Foustoucos, E., Andronikos, T. and Afrati, F., On temporal logic versus Datalog. Theor. Comput. Sci. 303 (2003) 103–133. CrossRef
M. Jurdzinski, Small progress measures for solving parity games. Proc. STACS'2000 (2000) 290–301.
M. Jurdzinski, M. Paterson and U. Zwick, A Deterministic subexponential algorithm for solving parity games. Proc. SODA (2006) 117–123.
Kozen, D., Results on the propositional µ-calculus. Theor. Comput. Sci. 27 (1983) 333–354. CrossRef
The, A. Mader modal µ-calculus, model-checking, equations systems and Gauss elimination. TACAS 95 (1995) 44–57.
Park, D., Finiteness is µ-ineffable. Theor. Comput. Sci. 3 (1976) 173–181. CrossRef
Seidl, H., Fast and simple nested fixpoints. Inform. Process. Lett. 59 (1996) 303–308. CrossRef
A. Vincent, Conception et réalisation d'un vérificateur de modèles AltaRica. Ph.D. Thesis, LaBRI, University of Bordeaux 1 (2003) http://altarica.labri.fr/Doc/Biblio/Author/VINCENT-A.html