On Expressiveness and Complexity in Real-Time Model Checking

Metric Interval Temporal Logic ( MITL ) is a popular formalism for expressing real-time specifications. This logic achieves decidability by restricting the precision of timing constraints, in particular, by banning so-called punctualspecifications. In this paper we introduce a significantly more expressive logic that can express a wide variety of punctual specifications, but whose model-checking problem has the same complexity as that of MITL . We conclude that for model checking the most commonly occurring specifications, such as invariance and bounded response, punctuality can be accommodated at no cost.

[1]  Mark Reynolds.  The complexity of temporal logic over the reals , 2010, Ann. Pure Appl. Log..

[2]  Thomas A. Henzinger,et al.  It's About Time: Real-Time Logics Reviewed , 1998, CONCUR.

[3]  Joël Ouaknine,et al.  On Metric Temporal Logic and Faulty Turing Machines , 2006, FoSSaCS.

[4]  Carsten Lutz,et al.  Quantitative temporal logics over the reals: PSpace and below , 2007, Inf. Comput..

[5]  Joseph Sifakis,et al.  Tools and Applications II: The IF Toolset , 2004 .

[6]  Jirí Srba,et al.  Comparing the Expressiveness of Timed Automata and Timed Extensions of Petri Nets , 2008, FORMATS.

[7]  Robert de Simone,et al.  CONCUR'98 Concurrency Theory , 1998, Lecture Notes in Computer Science.

[8]  Thomas A. Henzinger,et al.  The benefits of relaxing punctuality , 1991, JACM.

[9]  Alex K. Simpson,et al.  Computational Adequacy in an Elementary Topos , 1998, CSL.

[10]  Dejan Nickovic,et al.  From MITL to Timed Automata , 2006, FORMATS.

[11]  Joël Ouaknine,et al.  The Cost of Punctuality , 2007, 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007).

[12]  Amir Pnueli,et al.  The Glory of the Past , 1985, Logic of Programs.

[13]  Pierre Wolper,et al.  Constructing Automata from Temporal Logic Formulas: A Tutorial , 2002, European Educational Forum: School on Formal Methods and Performance Analysis.

[14]  Pierre-Yves Schobbens,et al.  The Regular Real-Time Languages , 1998, ICALP.

[15]  Yoram Hirshfeld,et al.  Timer formulas and decidable metric temporal logic , 2005, Inf. Comput..

[16]  Véronique Cortier,et al.  Flatness Is Not a Weakness , 2000, CSL.

[17]  Stéphane Demri,et al.  On the freeze quantifier in constraint LTL: decidability and complexity , 2005, 12th International Symposium on Temporal Representation and Reasoning (TIME'05).

[18]  Wa Halang,et al.  REAL-TIME SYSTEMS .2. , 1989 .

[19]  Ron Koymans,et al.  Specifying real-time properties with metric temporal logic , 1990, Real-Time Systems.

[20]  Rajeev Alur,et al.  Decision Problems for Timed Automata: A Survey , 2004, SFM.

[21]  Thomas A. Henzinger,et al.  Logics and Models of Real Time: A Survey , 1991, REX Workshop.

[22]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[23]  Rajeev Alur,et al.  A Theory of Timed Automata , 1994, Theor. Comput. Sci..

[24]  Robin Milner,et al.  Theories for the Global Ubiquitous Computer , 2004, FoSSaCS.

[25]  Thomas A. Henzinger,et al.  Real-Time Logics: Complexity and Expressiveness , 1993, Inf. Comput..