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Hardware-software co-synthesis of an embedded system requires mapping of its specifications into hardware and software modules such that its real-time and other constraints are met. Embedded system specifications are generally represented by acyclic task graphs. Many embedded system applications are characterized by aperiodic as well as periodic task graphs. Aperiodic task graphs can arrive for execution at any time and their resource requirements vary depending on how their constituent tasks and edges are allocated. Traditional approaches based on a fixed architecture coupled with slack stealing and/or on-line determination of how to serve aperiodic task graphs are not suitable for embedded systems with hard real-time constraints, since they cannot guarantee that such constraints would always be met. In this paper, we address the problem of concurrent co-synthesis of aperiodic and periodic specifications of embedded systems. We estimate the resource requirements of aperiodic task graphs and allocate execution slots on processing elements and communication links for executing them. Our approach guarantees that the deadlines of both aperiodic and periodic task graphs are always met. We have observed that simultaneous consideration of aperiodic task graphs while performing co-synthesis of periodic task graphs is vital for achieving superior results compared to the traditional slack stealing and dynamic scheduling approaches. To the best of our knowledge, this is the first co-synthesis algorithm which provides simultaneous support of periodic and aperiodic task graphs with hard real-time constraints. Application of the proposed algorithm to several examples from real-life telecom transport systems shows that up to 28% and 34% system cost savings are possible over co-synthesis algorithms which employ slack stealing and rate-monotonic scheduling, respectively.