Final answer:
The minimum number of page frames required for a running process in a virtual memory environment is determined by the instruction set architecture, which identifies the minimum working set necessary for execution.
Step-by-step explanation:
The question asks about the minimum number of page frames that must be allocated to a running process in a virtual memory environment. In such an environment, a virtual address space is divided into pages, which are then mapped to frames of physical memory. The answer to this question is highly dependent on the specific needs of a process, but at the very least, it needs enough frames to hold the process's minimum working set to allow for its execution without constant page faults.
This minimum working set is usually determined by the particular requirements of the process's instruction set architecture (ISA). The ISA defines the number of pages needed to store the process's instructions and data for active regions such as the stack, the heap and any other regions necessary for its execution. While the physical memory size, page size and the number of processes in memory may all influence performance and the allocation of memory, they are not direct determinants of the minimum number of frames required. Knowledge of the instruction set architecture allows for a calculation of the minimum resource needs for a process so that it can run properly.