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In mathematical logic and theoretical computer science, a register machine is a generic class of abstract machines used in a manner similar to a Turing machine. All the models are Turing equivalent. The register machine gets its name from its use of one or more "registers". In contrast to the tape and head used by a Turing machine, the model uses multiple, uniquely addressed registers, each of which holds a single positive integer. There are at least four sub-classes found in literature, here listed from most primitive to the most like a computer: Counter machine – the most primitive and reduced theoretical model of a computer hardware. Lacks indirect addressing. Instructions are in the finite state machine in the manner of the Harvard architecture. Pointer machine – a blend of counter machine and RAM models. Less common and more abstract than either model. Instructions are in the finite state machine in the manner of the Harvard architecture. Random-access machine (RAM) – a counter machine with indirect addressing and, usually, an augmented instruction set. Instructions are in the finite state machine in the manner of the Harvard architecture. Random-access stored-program machine model (RASP) – a RAM with instructions in its registers analogous to the Universal Turing machine; thus it is an example of the von Neumann architecture. But unlike a computer, the model is idealized with effectively infinite registers (and if used, effectively infinite special registers such as an accumulator). Compared to a computer, the instruction set is much reduced in number and complexity. Any properly defined register machine model is Turing equivalent. Computational speed is very dependent on the model specifics. In practical computer science, a similar concept known as a virtual machine is sometimes used to minimise dependencies on underlying machine architectures. Such machines are also used for teaching. The term "register machine" is sometimes used to refer to a virtual machine in textbooks.

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Computability is the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is closely linked to the existence of an algorithm to solve the problem. The most widely studied models of computability are the Turing-computable and μ-recursive functions, and the lambda calculus, all of which have computationally equivalent power.

Random-access machine

In computer science, random-access machine (RAM) is an abstract machine in the general class of register machines. The RAM is very similar to the counter machine but with the added capability of 'indirect addressing' of its registers. Like the counter machine, The RAM has its instructions in the finite-state portion of the machine (the so-called Harvard architecture). The RAM's equivalent of the universal Turing machine with its program in the registers as well as its data is called the random-access stored-program machine or RASP.