A processor that is configured to perform parallel operations in a computer system where one or more memory hazards may be present is described. An instruction fetch unit within the processor is configured to fetch instructions for detecting one or more critical memory hazards between memory addresses if memory operations are performed in parallel on multiple addresses corresponding to at least a partial vector of addresses. Note that critical memory hazards include memory hazards that lead to different results when the memory addresses are processed in parallel than when the memory addresses are processed sequentially. Furthermore, an execution unit within the processor is configured to execute the instructions for detecting the one or more critical memory hazards.