A Duration Calculus with Infinite Intervals

This paper introduces infinite intervals into the Duration Calculus [33]. The extended calculus defines a state duration over an infinite interval by a property which specifies the limit of the state duration over finite intervals, and excludes the description operator. Thus the calculus can be established without involvement of unpleasant calculation of infinity. With limits of state durations, one can treat conventional liveness and fairness, and can also measure liveness and fairness through properties of limits. Including both finite and infinite intervals, the calculus can, in a simple manner, distinguish between terminating behaviour and nonterminating behaviour, and therefore directly specify and reason about sequentiality.

[1]  Amir Pnueli,et al.  A Choppy Logic , 1986, LICS.

[2]  Yde Venema,et al.  A Modal Logic for Chopping Intervals , 1991, J. Log. Comput..

[3]  Michael R. Hansen,et al.  Decidability and Undecidability Results for Duration Calculus , 1993, STACS.

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

[5]  David Lorge Parnas,et al.  A Formal Approach to Computer Systems Requirements Documentation , 1992, Hybrid Systems.

[6]  Ben C. Moszkowski,et al.  Compositional reasoning about projected and infinite time , 1995, Proceedings of First IEEE International Conference on Engineering of Complex Computer Systems. ICECCS'95.

[7]  Yongqiang Sun,et al.  A Calculus for Hybrid Sampled Data Systems , 1994, FTRTFT.

[8]  Michael R. Hansen,et al.  A Real-Time Duration Semantics for Circuits , 1992 .

[9]  Anders P. Ravn,et al.  Towards a calculus of systems dependability , 1992 .

[10]  H. Weyl Mathematics and Logic , 1946 .

[11]  Michael R. Hansen,et al.  Semantics and Completeness of Duration Calculus , 1991, REX Workshop.

[12]  Joseph Sifakis,et al.  Integration Graphs: A Class of Decidable Hybrid Systems , 1992, Hybrid Systems.

[13]  C. A. R. Hoare,et al.  Communicating sequential processes , 1978, CACM.

[14]  A. TUSTIN,et al.  Automatic Control Systems , 1950, Nature.

[15]  Jens Ulrik Skakkebwk Liveness and Fairness in Duration Calculus , 1994 .

[16]  Anders P. Ravn,et al.  Specifying and Verifying Requirements of Real-Time Systems , 1993, IEEE Trans. Software Eng..

[17]  Anders P. Ravn,et al.  Duration Specifications for Shared Processors , 1992, FTRTFT.

[18]  Ben C. Moszkowski Some Very Compositional Temporal Properties , 1994, PROCOMET.

[19]  Anders P. Ravn,et al.  An Extended Duration Calculus for Hybrid Real-Time Systems , 1992, Hybrid Systems.

[20]  Michael R. Hansen,et al.  Finite Divergence , 1995, Theor. Comput. Sci..

[21]  Chaochen Zhou Linear Duration Invariants , 1994, FTRTFT.

[22]  Ben C. Moszkowski,et al.  A Temporal Logic for Multilevel Reasoning about Hardware , 1985, Computer.

[23]  Jens Ulrik Skakkebæk Liveness and Fairness in Duration Calculus , 1994, CONCUR.

[24]  Ji Wang,et al.  Formal Design of Hybrid Systems , 1994, FTRTFT.

[25]  A. Ravn,et al.  A Probabilistic Duration Calculus , 1992 .

[26]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[27]  Virgil C. Aldrich,et al.  The Philosophy of Bertrand Russell , 1945 .

[28]  Anders P. Ravn,et al.  Specification Of Embedded, Real-time Systems , 1992, Fourth Euromicro workshop on Real-Time Systems.

[29]  Jifeng He,et al.  Time interval semantics and implementation of a real-time programming language , 1992, Fourth Euromicro workshop on Real-Time Systems.

[30]  Chaochen Zhou,et al.  A Case Study of Optimization , 1995, Comput. J..

[31]  Zhou Chaochen,et al.  Duration Calculi: An overview , 1993 .

[32]  Benjamin C. Kuo,et al.  AUTOMATIC CONTROL SYSTEMS , 1962, Universum:Technical sciences.

[33]  Zhou Chaochen,et al.  A mean value calculus of durations , 1994 .

[34]  Natarajan Shankar,et al.  Towards a Duration Calculus Proof Assistant in PVS , 1994, FTRTFT.

[35]  Hermann Weyl,et al.  Mathematics and Logic: A brief survey serving as preface to a review ofThe Philosophy of Bertrand Russell , 1946 .