From continuous specification to discrete design.

The paper presents a syntactical approach to designing real-time distributed systems that can handle both continuous time and discrete time models in a uniform logical framework. We approximate continuous state variables by discrete ones and formalise the relationship between them. The requirements of a real-time system are specified as a formula over continuous state variables. Then we derive a discrete design of a digital controller as formula over discrete state variables that makes the system to satisfy the continuous specification under some assumptions about the behaviour of the environment and the relationship between continuous state variables and discrete state variables. We provide rules useful for refining and verifying the correctness of a design syntactically.