Revisiting Timed Specification Theories: A Linear-Time Perspective
This work addresses the challenge of designing reliable real-time systems with critical timing constraints, offering a formal framework for component-based development, though it appears incremental based on earlier work.
The authors tackled the problem of compositional design for real-time systems by proposing a specification theory for timed automata that supports substitutive refinement and operations like parallel composition and quotient. They introduced a weakest congruence preserving safety and bounded liveness properties, characterized by linear-time semantics such as timed-traces and timed-strategies.
We consider the setting of component-based design for real-time systems with critical timing constraints. Based on our earlier work, we propose a compositional specification theory for timed automata with I/O distinction, which supports substitutive refinement. Our theory provides the operations of parallel composition for composing components at run-time, logical conjunction/disjunction for independent development, and quotient for incremental synthesis. The key novelty of our timed theory lies in a weakest congruence preserving safety as well as bounded liveness properties. We show that the congruence can be characterised by two linear-time semantics, timed-traces and timed-strategies, the latter of which is derived from a game-based interpretation of timed interaction.