Probabilistic models of random behaviours of concurrent systems I

The paper presents a universal basis for dening and analysing random behaviours of concurrent systems. It describes how to represent the behaviour of a concurrent system as a directed complete partially ordered set of initial segments of its possible runs, and how to represent the possible random nature of such a behaviour as a probability space on the set of possible full runs. In particular, it describes how a probability space which represents a random behaviour of a concurrent system can be constructed as a projective limit of a projective system of probability spaces representing initial parts of such a behaviour.

[1]  P. Meyer Probability and potentials , 1966 .

[2]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[3]  S. Lane Categories for the Working Mathematician , 1971 .

[4]  Robin Milner,et al.  Synthesis of Communicating Behaviour , 1978, MFCS.

[5]  K. Parthasarathy Introduction to Probability and Measure , 1979 .

[6]  C. A. Petri Introduction to General Net Theory , 1979, Advanced Course: Net Theory and Applications.

[7]  K. Hofmann,et al.  A Compendium of Continuous Lattices , 1980 .

[8]  Micha Sharir,et al.  Termination of Probabilistic Concurrent Program , 1983, TOPL.

[9]  Helmut Plünnecke K-density, N-density and finiteness properties , 1984, European Workshop on Applications and Theory in Petri Nets.

[10]  Amir Pnueli,et al.  Applications of Temporal Logic to the Specification and Verification of Reactive Systems: A Survey of Current Trends , 1986, Current Trends in Concurrency.

[11]  C. Jones,et al.  A probabilistic powerdomain of evaluations , 1989, [1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science.

[12]  Gordon D. Plotkin,et al.  Configuration structures , 1995, Proceedings of Tenth Annual IEEE Symposium on Logic in Computer Science.

[13]  Abbas Edalat,et al.  An Extension Result for Continuous Valuations , 2000 .

[14]  Manfred Droste,et al.  Continuous Petri Nets and Transition Systems , 2001, Unifying Petri Nets.

[15]  Józef Winkowski,et al.  An algebraic characterization of independence of Petri net processes , 2003, Inf. Process. Lett..

[16]  Marta Z. Kwiatkowska,et al.  Model checking for probability and time: from theory to practice , 2003, 18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings..

[17]  Józef Winkowski,et al.  Towards a Framework for Modelling Systems with Rich Internal Structures of States and Processes , 2005, Fundam. Informaticae.

[18]  B. Schutter Models for Hybrid Systems , 2005 .

[19]  Joost Engelfriet,et al.  Branching processes of Petri nets , 1991, Acta Informatica.

[20]  Glynn Winskel,et al.  Probabilistic event structures and domains , 2006, Theor. Comput. Sci..

[21]  Józef Winkowski,et al.  Towards a Framework for Modelling Behaviours of Hybrid Systems , 2007, Fundam. Informaticae.

[22]  Nancy A. Lynch,et al.  Observing Branching Structure through Probabilistic Contexts , 2007, SIAM J. Comput..

[23]  Nancy A. Lynch,et al.  Trace-Based Semantics for Probabilistic Timed I/O Automata , 2007, HSCC.

[24]  Józef Winkowski,et al.  An Algebraic Framework for Defining Random Concurrent Behaviours , 2008, Fundam. Informaticae.

[25]  Józef Winkowski,et al.  An Algebraic Framework for Defining Behaviours of Concurrent Systems. Part 1: The Constructive Presentation , 2009, Fundam. Informaticae.