Gerald J. Popek, from the University of California at Los Angeles, discusses the hardware requirements for virtual machine systems. He notes that while virtual machine techniques are valuable for operating system development, program portability, and running multiple systems concurrently, many third-generation computers, like the DEC PDP-10, cannot support them. Popek defines a virtual machine with efficiency, isolation, and identical behavior, and develops a model of third-generation computers with a processor having supervisor and user modes, memory with simple protection, and a trap facility. He characterizes instruction behavior in this context. Robert P. Goldberg, from Honeywell Information Systems and Harvard University, applies formal techniques to derive precise conditions for determining if a computer architecture can support virtual machines. The paper's major theorem states that a virtual machine system can be constructed if and only if certain properties of the real machine's instruction set are met. A constructive proof is provided, explaining underlying ideas. The conditions are simple and can be used to evaluate existing hardware or guide new machine design. Related concepts, such as hybrid virtual machines and recursive virtualization, are also described. The paper concludes by noting model simplifications, possible extensions, and the usefulness of the formal approach.Gerald J. Popek, from the University of California at Los Angeles, discusses the hardware requirements for virtual machine systems. He notes that while virtual machine techniques are valuable for operating system development, program portability, and running multiple systems concurrently, many third-generation computers, like the DEC PDP-10, cannot support them. Popek defines a virtual machine with efficiency, isolation, and identical behavior, and develops a model of third-generation computers with a processor having supervisor and user modes, memory with simple protection, and a trap facility. He characterizes instruction behavior in this context. Robert P. Goldberg, from Honeywell Information Systems and Harvard University, applies formal techniques to derive precise conditions for determining if a computer architecture can support virtual machines. The paper's major theorem states that a virtual machine system can be constructed if and only if certain properties of the real machine's instruction set are met. A constructive proof is provided, explaining underlying ideas. The conditions are simple and can be used to evaluate existing hardware or guide new machine design. Related concepts, such as hybrid virtual machines and recursive virtualization, are also described. The paper concludes by noting model simplifications, possible extensions, and the usefulness of the formal approach.