Hybrid logics on linear structures: expressivity and complexity

We investigate expressivity and complexity of hybrid logics on linear structures. Hybrid logics are an enrichment of modal logics with certain first-order features which are algorithmically well behaved. Therefore, they are well suited for the specification of certain properties of computational systems. We show that hybrid logics are more expressive than usual modal and temporal logics on linear structures, and exhibit a hierarchy of hybrid languages. We determine the complexities of the satisfiability problem for these languages and define an existential fragment of hybrid logic for which satisfiability is still NP-complete. Finally, we examine the linear time model checking problem for hybrid logics and its complexity.

[1]  Abraham Robinson,et al.  Elementary properties of ordered abelian groups , 1960 .

[2]  A. Nakamura,et al.  On the size of refutation Kripke models for some linear modal and tense logics , 1980 .

[3]  Marco Pistore,et al.  Improving the Encoding of LTL Model Checking into SAT , 2002, VMCAI.

[4]  Mark Reynolds,et al.  The complexity of the temporal logic with "until" over general linear time , 2003, J. Comput. Syst. Sci..

[5]  E. Clarke,et al.  Symbolic model checking using SAT procedures instead of BDDs , 1999, Proceedings 1999 Design Automation Conference (Cat. No. 99CH36361).

[6]  Maarten Marx,et al.  Hybrid logics: characterization, interpolation and complexity , 2001, Journal of Symbolic Logic.

[7]  M. de Rijke,et al.  Modal Logic , 2001, Cambridge Tracts in Theoretical Computer Science.

[8]  D. Gabbay,et al.  Temporal Logic Mathematical Foundations and Computational Aspects , 1994 .

[9]  J. R. Büchi.  On a Decision Method in Restricted Second Order Arithmetic , 1990 .

[10]  R. McNaughton.  Review: J. Richard Buchi, Weak Second-Order Arithmetic and Finite Automata; J. Richard Buchi, On a Decision Method in Restricted second Order Arithmetic , 1963, Journal of Symbolic Logic.

[11]  Marco Benedetti,et al.  Bounded Model Checking for Past LTL , 2003, TACAS.

[12]  Maarten Marx,et al.  The Computational Complexity of Hybrid Temporal Logics , 2000, Log. J. IGPL.

[13]  A. Prasad Sistla,et al.  The complexity of propositional linear temporal logics , 1982, STOC '82.

[14]  Patrick Blackburn,et al.  Hybrid languages , 1995, J. Log. Lang. Inf..

[15]  Nicolas Markey.  Past is for free: on the complexity of verifying linear temporal properties with past , 2003, Acta Informatica.

[16]  Maarten Marx,et al.  A Road-Map on Complexity for Hybrid Logics , 1999, CSL.

[17]  Philippe Schnoebelen,et al.  The Complexity of Propositional Linear Temporal Logics in Simple Cases , 1998, Inf. Comput..

[18]  Alasdair Urquhart,et al.  Temporal Logic , 1971 .