Pointer machine

In theoretical computer science a pointer machine is an "atomistic" abstract computational machine model akin to the Random access machine.

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. 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:

But Ben-Amram add more:

Use of the model in complexity theory: van Emde Boas (1990) expresses concern that this form of abstract model is:

Gurevich 1988 also expresses concern:

The fact that, in §3 and §4 (pp. 494–497), Schönhage himself (1980) demonstrates the real-time equivalences of his two Random Access Machine models "RAM0" and "RAM1" leads one to question the necessity of the SMM for complexity studies.

Potential uses for the model: However, Schönhage (1980) demonstrates in his §6, Integer-multiplication in linear time. And Gurevich wonders whether or not the "parallel KU machine" "resembles somewhat the human brain" (Gurevich (1988) p. 5)

Schönhage's SMM model seems to be the most common and most accepted. It is quite unlike the register machine model and other common computational models e.g. the tape-based Turing machine or the labeled holes and indistinguishable pebbles of the counter machine.

...
Wikipedia