Store Buffer Reduction with MMUs: Complete Paper-and-pencil Proof

A fundamental problem in concurrent system design is to identify flexible programming disciplines under which weak memory models provide sequential consistency. For x86-TSO, a suitable reduction theorem for threads that communicate only through shared memory was given by Cohen and Schirmer [5]. However, this theorem cannot handle programs that edit their own page tables (e.g. memory mangers, hypervisors, and some device drivers). The problem lies in the interaction between a program thread and the hardware MMU that provides its address translation: the MMU cannot be treated as a separate thread (since it implicitly communicates with the program thread), nor as part of the program thread itself (since MMU reads do not snoop the store buffer of the program thread). We generalize the Cohen-Schirmer reduction theorem to handle programs that edit their page tables. The added conditions prevent the MMU of a thread from walking page table entries owned by other threads.