In theoretical computer science, a pointer machine is an atomistic abstract computational machine model akin to the random-access machine. A pointer algorithm could also be an algorithm restricted to the pointer machine model.
Depending on the type, a pointer machine may be called a linking automaton, a KU-machine, an SMM, an atomistic LISP machine, a tree-pointer machine, etc. (cf Ben-Amram 1995). At least three major varieties exist in the literature—the Kolmogorov-Uspenskii model (KUM, KU-machine), the Knuth linking automaton, and the Schönhage Storage Modification Machine model (SMM). The SMM seems to be the most common.
From its "read-only tape" (or equivalent) a pointer machine receives input—bounded symbol-sequences ("words") made of at least two symbols e.g. { 0, 1 } — and it writes output symbol-sequences on an output "write-only" tape (or equivalent). To transform a symbol-sequence (input word) to an output symbol-sequence the machine is equipped with a "program"—a finite-state machine (memory and list of instructions). Via its state machine the program reads the input symbols, operates on its storage structure—a collection of "nodes" (registers) interconnected by "edges" (pointers labelled with the symbols e.g. { 0, 1 }), and writes symbols on the output tape.
Pointer machines cannot do arithmetic in normal ways. Computation proceeds only by reading input symbols, modifying and doing various tests on its storage structure—the pattern of nodes and pointers, and outputting symbols based on the tests. "Information" is in the storage structure.
Both Gurevich and Ben-Amram list a number of very similar "atomistic" models of "abstract machines"; Ben-Amram believes that the 6 "atomistic models" must be distinguished from "High-level" models. This article will discuss the following 3 atomistic models in particular:
Schönhage's storage modification machines (SMM),
Kolmogorov–Uspenskii machines (KUM or KU-Machines),
Knuth's "linking automaton"
But Ben-Amram adds more:
Atomistic pure-LISP machine (APLM)
Atomistic full-LISP machine (AFLM),
General atomistic pointer machines,
Jone's I language (two types)
Use of the model in complexity theory:
van Emde Boas (1990) expresses concern that this form of abstract model is:
"an interesting theoretical model, but .
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A counter machine is an abstract machine used in a formal logic and theoretical computer science to model computation. It is the most primitive of the four types of register machines. A counter machine comprises a set of one or more unbounded registers, each of which can hold a single non-negative integer, and a list of (usually sequential) arithmetic and control instructions for the machine to follow. The counter machine is typically used in the process of designing parallel algorithms in relation to the mutual exclusion principle.
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.
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.
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