Generalized Synchronization Trees

This paper develops a generalized theory of synchronization trees. In their original formulation, synchronization trees modeled the behavior of nondeterministic discrete-time reactive systems and served as the foundational theory upon which process algebra was based. In this work, a more general notion of tree is proposed that is intended to support the modeling of systems with a variety of notions of time, including continuous and hybrid versions. (Bi)simulation is also studied, and it is shown that two notions that coincide in the discrete setting yield different relations in the generalized framework. A CSP-like parallel composition operator for generalized trees is defined as a means of demonstrating the support for compositionality the new framework affords.

[1]  Huei Peng,et al.  Shortest path stochastic control for hybrid electric vehicles , 2008 .

[2]  William C. Rounds,et al.  On the Relationship between Scott Domains, Synchronization Trees, and Metric Spaces , 1985, Inf. Control..

[3]  Paulo Tabuada,et al.  Bisimulation relations for dynamical, control, and hybrid systems , 2005, Theor. Comput. Sci..

[4]  Peter Aczel,et al.  Non-well-founded sets , 1988, CSLI lecture notes series.

[5]  J. Bergstra,et al.  Handbook of Process Algebra , 2001 .

[6]  Thomas A. Henzinger,et al.  Hybrid Systems: Computation and Control , 1998, Lecture Notes in Computer Science.

[7]  J. Willems.  On interconnections, control, and feedback , 1997, IEEE Trans. Autom. Control..

[8]  Pjl Pieter Cuijpers.  Prefix orders as a general model of dynamics , 2013 .

[9]  A.J. van der Schaft,et al.  Bisimulation as congruence in the behavioral setting , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[10]  Samson Abramsky,et al.  A Domain Equation for Bisimulation , 1991, Inf. Comput..

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

[12]  Paulo Tabuada,et al.  On Simulations and Bisimulations of General Flow Systems , 2007, HSCC.

[13]  Antoine Girard,et al.  Approximate Bisimulation: A Bridge Between Computer Science and Control Theory , 2011, Eur. J. Control.

[14]  Frits W. Vaandrager,et al.  Turning SOS Rules into Equations , 1994, Inf. Comput..

[15]  D. Sangiorgi.  Introduction to Bisimulation and Coinduction , 2011 .

[16]  David Park,et al.  Concurrency and Automata on Infinite Sequences , 1981, Theoretical Computer Science.

[17]  George J. Pappas,et al.  Unifying bisimulation relations for discrete and continuous systems , 2002 .