Duration Calculus: A Real-Time Semantic for B

Among the possible approaches for expressing real-time problems with the B method, two are dominant : the use of the usual B mechanisms to define real-time constraints on the one hand, and extending B through another formalism more adapted to the real-time context on the other hand. We define here a possible real-time semantic for B, by using a real-time logic (the duration calculus), and we illustrate how this extension affects the proof mechanism used to show the soundness of abstract machines.

[1]  Jacques Julliand,et al.  Approches formelles dans l'assistance au développement de logiciels , 2006 .

[2]  J. Oxford,et al.  Oxford , 1968, Leaving The Arena.

[3]  Dimitar P. Guelev,et al.  Completeness and Decidability of a Fragment of Duration Calculus with Iteration , 1999, ASIAN.

[4]  A. Tricoteaux,et al.  Laboratoire des Materiaux Avances Ceramiques, Universite de Valenciennes et du Hainaut Cambresis, , 2003 .

[5]  Yuri Gurevich,et al.  Logic in Computer Science , 1993, Current Trends in Theoretical Computer Science.

[6]  Chaochen Zhou,et al.  A Duration Calculus with Infinite Intervals , 1995, FCT.

[7]  Jean-Raymond Abrial,et al.  The B-book - assigning programs to meanings , 1996 .

[8]  Paul Benoit,et al.  Météor: A Successful Application of B in a Large Project , 1999, World Congress on Formal Methods.

[9]  Dorian Petit Génération automatique de composants logiciels sûrs à partir de spécifications formelles B , 2003 .

[10]  François Siewe,et al.  Deriving Real-Time Programs from Duration Calculus Specifications , 2001, CHARME.

[11]  Bruno Dutertre,et al.  Complete proof systems for first order interval temporal logic , 1995, Proceedings of Tenth Annual IEEE Symposium on Logic in Computer Science.

[12]  Michael R. Hansen,et al.  Duration Calculus: A Formal Approach to Real-Time Systems (Monographs in Theoretical Computer Science. an Eatcs Seris) , 2004 .

[13]  Michael R. Hansen,et al.  Duration calculus: Logical foundations , 1997, Formal Aspects of Computing.

[14]  Zhan Naijun Another formal proof for Deadline Driven Scheduler , 2000, Proceedings Seventh International Conference on Real-Time Computing Systems and Applications.

[15]  P. Pandya Specifying and Deciding Quantified Discrete-time Duration Calculus Formulae using DCVALID , 2000 .

[16]  Zhou Chaochen,et al.  Duration Calculus: A Formal Approach to Real-Time Systems , 2004 .

[17]  Thomas Marthedal Rasmussen,et al.  Interval logic. Proof theory and theorem proving , 2002 .

[18]  J. Davenport Editor , 1960 .

[19]  Constance L. Heitmeyer,et al.  A Benchmark for Comparing Different Approaches for Specifying and Verifying Real-Time Systems , 1993 .

[20]  Helen Treharne,et al.  Capturing timing requirements formally in AMN , 1999 .

[21]  R. P. Cook Seventh IEEE Workshop on Real-Time Operating Systems and Software , 1990 .

[22]  Geoff Sutcliffe,et al.  6th International Workshop on the Implementation of Logics , 2006 .

[23]  Constance L. Heitmeyer,et al.  Comparing different approaches for specifying and verifying real-time systems , 1993 .

[24]  Dang Van Hung Checking Timed Automata for Some Discretisable Duration Properties Checking Timed Automata for Some Discretisable Duration Properties , 1998 .

[25]  C. A. R. Hoare,et al.  A Calculus of Durations , 1991, Inf. Process. Lett..