We coalgebraically define a unified semantics for systems with an emphasis on the notion of time. Such a semantics intends to formalize system that underly system engineering (i.e. the discipline focusing on the integration mastery of large industrial systems).Moreover, we give a formal meaning to another important aspect of systems engineering: system requirements, constraining the expected properties of a system. To express such requirements, we define a logic that extends μ-calculus to our coalgebraic definition of systems. We establish an important property of this logic: adequacy.

We develop a unified functional formalism for modelling complex systems, that is to say systems that are composed of a number of heterogeneous components, including typically software and physical devices. Our approach relies on non-standard analysis that allows us to model continuous time in a discrete way. S ystems are defined as generalized Turing machines with temporized input, internal and output mechanisms. Behaviors of systems are represented by transfer functions. A transfer function is said to be implementable if it is associated with a system. This notion leads us to define a new class – which is natural in our framework – of computable functions on (usual) real numbers. We show that our definitions are robust: on one hand, the class of implementable transfer functions is closed under composition; on the other hand, the class of computable functions in our meaning includes analytical functions whose coefficients are computable in the usual way, and is closed under addition, multiplication, differentiation and integration. Our class of computable functions also includes solutions of dynamical and Hamiltonian systems defined by computable functions. Hence, our notion of system appears to take suitably into account physical systems.

We consider several hybrid ARQ (H-ARQ) control schemes for high speed downlink packet access (HSDPA) with 16 symbols quadrature amplitude modulation (16QAM). These schemes consist of a sequence of values for the X/sub rv/ parameter to be used at sequential retransmissions when a block is not decoded correctly. A choice of an H-ARQ control scheme influences two parameters: quality of service (QoS) and user equipment (UE) buffer requirements. Based on several link level simulations, we propose an optimal control scheme using maximum space, as well as two slightly suboptimal ones that allow to reduce the UE buffer size.