Rule Formats for Timed Processes

Abstract Building on previous work (15,8), this paper describes two syntactic ways of defining ‘well-behaved’ operational semantics for timed processes. In both cases, the semantic rules are derived from abstract operational rules for behaviour comonads and thus ensure congruence results. The first of them, a light-weight attempt using schematic rules , is shown to be sound , i.e., to indeed induce abstract rules as introduced in [8]. Then a second format, based on a new and very general kind of abstract rules, comonadic SOS (CSOS) , is presented which uses meta rules and is also complete , i.e., it characterises all possible CSOS rules for timed processes.

[1]  Joseph Sifakis,et al.  An Overview and Synthesis on Timed Process Algebras , 1991, REX Workshop.

[2]  Falk Bartels,et al.  GSOS for Probabilistic Transition Systems , 2002, CMCS.

[3]  Albert R. Meyer,et al.  Bisimulation can't be traced , 1988, POPL '88.

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

[5]  Gordon D. Plotkin,et al.  Towards a mathematical operational semantics , 1997, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science.

[6]  John Power,et al.  Combining a monad and a comonad , 2002, Theor. Comput. Sci..

[7]  Marcelo P. Fiore Fibred Models of Processes: Discrete, Continuous, and Hybrid Systems , 2000, IFIP TCS.

[8]  D. Turi,et al.  Functional Operational Semantics and its Denotational Dual , 1996 .

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

[10]  Marco Kick,et al.  Bialgebraic Modelling of Timed Processes , 2002, ICALP.

[11]  Reiko Heckel,et al.  Compositional SOS and beyond: a coalgebraic view of open systems , 2002, Theor. Comput. Sci..

[12]  Peter Aczel,et al.  A Final Coalgebra Theorem , 1989, Category Theory and Computer Science.

[13]  Gordon D. Plotkin,et al.  A structural approach to operational semantics , 2004, J. Log. Algebraic Methods Program..

[14]  John Power,et al.  Distributivity for endofunctors, pointed and co-pointed endofunctors, monads and comonads , 2000, CMCS.