Process algebra for hybrid systems

We propose a process algebra obtained by extending a combination of the process algebra with continuous relative timing from Baeten and Middelburg (Process Algebra with Timing, Springer, Berlin, 2002, Chapter 4), and the process algebra with propositional signals from Baeten and Bergstra (Theoret. Comput. Sci. 177 (1977) 381–405). The proposed process algebra makes it possible to deal with the behaviour of hybrid systems, i.e. systems in which the instantaneous state transitions caused by performing actions are alternated with continuous state evolutions. This process algebra has, in addition to equational axioms, rules to derive equations with the help of real analysis. © 2005 Elsevier B.V. All rights reserved.

[1]  Joseph Sifakis,et al.  The Algebra of Timed Processes, ATP: Theory and Application , 1994, Inf. Comput..

[2]  T. Henzinger,et al.  Algorithmic Analysis of Nonlinear Hybrid Systems , 1998, CAV.

[3]  Thomas A. Henzinger,et al.  HYTECH: a model checker for hybrid systems , 1997, International Journal on Software Tools for Technology Transfer.

[4]  Jos C. M. Baeten,et al.  Process Algebra with Timing: Real Time and Discrete Time , 1999, Handbook of Process Algebra.

[5]  Thomas A. Henzinger,et al.  The Algorithmic Analysis of Hybrid Systems , 1995, Theor. Comput. Sci..

[6]  Jan A. Bergstra,et al.  Real time process algebra with infinitesimals , 1993 .

[7]  A. W. Roscoe.  A classical mind: essays in honour of C. A. R. Hoare , 1994 .

[8]  Jan A. Bergstra,et al.  Algebra of timed frames , 1995, Int. J. Comput. Math..

[9]  Thomas A. Henzinger,et al.  Towards Refining Temporal Specifications into Hybrid Systems , 1992, Hybrid Systems.

[10]  Insup Lee,et al.  Compositional Refinement for Hierarchical Hybrid Systems , 2001, HSCC.

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

[12]  Jan A. Bergstra,et al.  Real space process algebra , 1991, Formal Aspects of Computing.

[13]  Kees Middelburg.  Process Algebra with Nonstandard Timing , 2002, Fundam. Informaticae.

[14]  Jan A. Bergstra,et al.  Located Actions in Process Algebra with Timing , 2004, Fundam. Informaticae.

[15]  Davide Sangiorgi,et al.  Communicating and Mobile Systems: the π-calculus, , 2000 .

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

[17]  Jos C. M. Baeten,et al.  Process Algebra , 2007, Handbook of Dynamic System Modeling.

[18]  Nancy A. Lynch,et al.  Hybrid I/O automata , 1995, Inf. Comput..

[19]  Jan A. Bergstra,et al.  Discrete time process algebra with silent step , 2000, Proof, Language, and Interaction.

[20]  Kees Middelburg,et al.  Truth of Duration Calculus Formulae in Timed Frames , 1998, Fundam. Informaticae.

[21]  Kees Middelburg,et al.  Variable binding operators in transition system specifications , 2000, J. Log. Algebraic Methods Program..

[22]  Jan A. Bergstra,et al.  Verification of an alternating bit protocol by means of process algebra , 1985, Mathematical Methods of Specification and Synthesis of Software Systems.

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

[24]  P. J. L. Cuijpers,et al.  Topological (Bi-)Simulation , 2004, CMCIM/GETCO@CONCUR.

[25]  Kees Middelburg.  An alternative formulation of operational conservativity with binding terms , 2003, J. Log. Algebraic Methods Program..

[26]  Kees Middelburg.  Revisiting timing in process algebra , 2003, J. Log. Algebraic Methods Program..

[27]  Jan A. Bergstra,et al.  The Algebra of Recursively Defined Processes and the Algebra of Regular Processes , 1984, ICALP.

[28]  Jan A. Bergstra,et al.  Discrete time process algebra , 1992, Formal Aspects of Computing.

[29]  Faron Moller,et al.  A Temporal Calculus of Communicating Systems , 1990, CONCUR.

[30]  Jos C. M. Baeten,et al.  Process Algebra with Timing , 2002, Monographs in Theoretical Computer Science. An EATCS Series.

[31]  Jim Davies,et al.  Timed CSP: Theory and Practice , 1991, REX Workshop.

[32]  Thomas A. Henzinger,et al.  Assume-Guarantee Reasoning for Hierarchical Hybrid Systems , 2001, HSCC.

[33]  Luca Aceto,et al.  Structural Operational Semantics , 1999, Handbook of Process Algebra.

[34]  Jan Joris Vereijken.  A Process Algebra for Hybrid Systems , 1999 .

[35]  Wang Yi,et al.  Real-Time Behaviour of Asynchronous Agents , 1990, CONCUR.

[36]  Jan Friso Groote,et al.  Analysis of three hybrid systems in timed µCRL , 2001, Sci. Comput. Program..

[37]  Jan A. Bergstra,et al.  Process Algebra with Propositional Signals , 1994, Theor. Comput. Sci..

[38]  Jos C. M. Baeten,et al.  A new equivalence for processes with timing. With an application to protocol verification , 2000 .

[39]  David de Frutos-Escrig,et al.  TIC: A timed calculus , 1993, Formal Aspects of Computing.

[40]  Thomas A. Henzinger,et al.  Beyond HYTECH: Hybrid Systems Analysis Using Interval Numerical Methods , 2000, HSCC.

[41]  Jan Friso Groote,et al.  Process algebra with guards: Combining Hoare logic with process algebra , 1994, Formal Aspects of Computing.

[42]  Thomas A. Henzinger,et al.  Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems , 1992, Hybrid Systems.

[43]  Michel A. Reniers,et al.  Hybrid process algebra , 2005, J. Log. Algebraic Methods Program..

[44]  Hosung Song,et al.  The Phi-Calculus: A Language for Distributed Control of Reconfigurable Embedded Systems , 2003, HSCC.

[45]  Jan A. Bergstra,et al.  Real time process algebra , 1991, Formal Aspects of Computing.

[46]  Thomas A. Henzinger,et al.  Automatic symbolic verification of embedded systems , 1993, 1993 Proceedings Real-Time Systems Symposium.

[47]  Matthew Hennessy,et al.  A Process Algebra for Timed Systems , 1995, Inf. Comput..

[48]  Thomas A. Henzinger,et al.  The theory of hybrid automata , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[49]  R. J. vanGlabbeek.  The linear time - branching time spectrum , 1990 .

[50]  Liang Chen,et al.  An Interleaving Model for Real-Time Systems , 1992, LFCS.

[51]  Jan A. Bergstra,et al.  Continuity controlled hybrid automata , 2004, J. Log. Algebraic Methods Program..

[52]  Jan A. Bergstra,et al.  Discrete Time Process Algebra and the Semantics of SDL , 1998, Handbook of Process Algebra.