The Relationships between Several Parallel Computation Models

The Parallel Random Access Machine (PRAM for short) is the most convenient and widely used model of parallel computation. Other, more complex models have also been studied. Examples include the Broadcast with Selective Reduction (or BSR) and the Reconfigurable Multiple Bus Machine (or RMBM). While the PRAM and the BSR are shared memory models, the RMBM accomplishes the communication between processors using buses. In this thesis we identify surprising relationships between these models: We show that several variants are equivalent with each other in a strong sense, but we also establish strict distinctions between the other variants. Some models are folklorically considered feasible and some others are not considered so. We find a delimitation that matches the folklore, but we also find important (and intriguing) equivalencies.