Certifying real-time guarantees for imperative programs is a critical challenge in embedded systems and cyber-physical applications. However, existing certified compilers lack the capability to accurately translate high-level timing abstractions into low-level executable code while preserving temporal semantics. This paper introduces a category-theoretic framework to model time-sensitive programs, leveraging monads and comonads to capture both the production and observation of temporal effects. Our methodology is formalized in the Rocq proof assistant, providing a foundation for the development of a certified compiler capable of preserving real-time constraints across compilation stages. By abstracting timing effects categorically, this work bridges the gap between theoretical program semantics and practical real-time certification, offering a principled path toward verified compilation for time-critical systems.

In this paper, we study a subclass of constraint automata with local variables. The fragment denotes an executable subset of constraint automata for which synchronization and data constraints are expressed in an imperative guarded command style, instead of a denotational style as in the coordination language Reo. To demonstrate the executability property, we provide a translation scheme from symbolic constraint automata to Promela, the language of the model checker Spin. As a proof of concept, we model in Reo a software defined network circuit, and use the Spin model checker to verify that our model satisfies some temporal properties.

Composition is an important feature of a specification language, as it enables the design of a complex system in terms of a product of its parts. Decomposition is equally important in order to reason about structural properties of a system. Usually, however, a system can be decomposed in more than one way, each optimizing for a different set of criteria. We extend an algebraic component-based model for cyber-physical systems to reason about decomposition. In this model, components compose using a family of algebraic products, and decompose, under some conditions, given a corresponding family of division operators. We use division to specify invariant of a system of components, and to model desirable updates. We apply our framework to design a cyber-physical system consisting of robots moving on a shared field, and identify desirable updates using our division operator.

We propose a component-based semantic model for Cyber-Physical Systems (CPSs) wherein the notion of a component abstracts the internal details of both cyber and physical processes, to expose a uniform semantic model of their externally observable behaviors expressed as sets of sequences of observations. We introduce algebraic operations on such sequences to model different kinds of component composition. These composition operators yield the externally observable behavior of their resulting composite components through specifications of interactions of the behaviors of their constituent components, as they, e.g., synchronize with or mutually exclude each other's alternative behaviors. Our framework is expressive enough to allow articulation of properties that coordinate desired interactions among composed components within the framework, also as component behavior. We demonstrate the usefulness of our formalism through examples of coordination properties in a CPS consisting of two robots interacting through shared physical resources.