Heterogeneous systems, in which a CPU and an accelerator can execute together while sharing memory, are becoming popular in several computing sectors. Nowadays, programmers can split their computation into multiple specialised threads that can take advantage of each specialised component. FPGAs are popular accelerators with configurable logic for various tasks, and hardware manufacturers are developing platforms with tightly integrated multicore CPUs and FPGAs. In such tightly integrated platforms, the CPU threads and the FPGA threads access shared memory locations in a fine-grained manner. However, architectural optimisations will lead to instructions being observed out of order by different cores. The programmers must consider these reorderings for correct program executions.

Memory models can aid in reasoning about these complex systems since they can be used to explore guarantees regarding the systems' behaviours. These models are helpful for low-level programmers, compiler writers, and designers of analysis tools. Memory models are specified according to two main paradigms: operational and axiomatic. An operational model is an abstract representation of the actual machine, described by states that represent idealised components such as buffers and queues, and the legal transitions between these states. Axiomatic models define relations between memory accesses to constrain the allowed and disallowed behaviours.

This dissertation makes the following main contributions: an operational model of a CPU/FPGA system, an axiomatic one and an exploration of simulation techniques for operational models. The operational model is implemented in C and validated using all the behaviours described in the available documentation. We will see how the ambiguities from the documentation can be clarified by running tests on the hardware and consulting with the designers. Finally, to demonstrate the model's utility, we reason about a producer/consumer buffer implemented across the CPU and the FPGA.

The simulation of axiomatic models can be orders of magnitude faster than operational models. For this reason, we also provide an axiomatic version of the memory model. This model allows us to generate small concurrent programs to reveal whether a specific memory model behaviour can occur. However, synthesising a single test for the FPGA requires significant time and prevents us from directly running many tests. To overcome this issue, we develop a soft-core processor that allows us to quickly run large numbers of such tests and gain higher confidence in the accuracy of our models.

The simulation of the operational model faces a path-explosion problem that limits the exploration of large models. Observing that program analysis tools tackle a similar path-explosion problem, we investigate the idea of reducing the decision problem of ``whether a given memory model allows a given behaviour'' to the decision problem of ``whether a given C program is safe'', which can be handled by a variety of off-the-shelf tools. Using this approach, we can simulate our model more deeply and gain more confidence in its accuracy.