Recent technological advances have led to an increasing gap between memory and processor performance, since memory bandwidth is progressing at a much slower pace than processor bandwidth. Pre-fetching techniques are traditionally used to bridge this gap and achieve high processor utilization while tolerating high memory latencies. Following this trend, new computational models have been proposed to split task execution in two consecutive phases: a memory phase in which the required instructions and data are pre-fetched to local memory (M-phase), and an execution phase in which the task is executed with no memory contention (C-phase). Decoupling memory and execution phases not only simplifies the timing analysis, but also allows a more efficient (and predictable) pipelining of memory and execution phases through proper co-scheduling algorithms. This paper takes a further step towards the design of smart co-scheduling algorithms for sporadic real-time tasks complying with the memory-computation (M/C) model, by proposing a theoretical framework aimed at tightly characterizing the schedulability improvement obtainable with the adopted M/C task model on single-core systems. In particular, a critical instant is identified for M/C tasks scheduled with fixed priority and an exact response time analysis with pseudo-polynomial complexity is provided. Then, we investigate the problem of priority assignment for M/C tasks, showing that a necessary condition to achieve optimality is to allow different priorities for the two phases. Our experiments show that the proposed techniques provide a significant schedulability improvement with respect to classic execution models, placing an important building block towards the design of more efficient partitioned multi-core systems.