Toroidal inductors and transformers: Difference between revisions

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In [[computation theory]], the '''Blum–Shub–Smale machine''', or '''BSS machine''', is a model of computation introduced by [[Lenore Blum]], [[Michael Shub]] and [[Stephen Smale]], intended to describe computations over the real numbers. Essentially, a BSS machine is a [[Random Access Machine]] with registers that can store arbitrary real numbers and that can compute rational functions over reals at unit cost. It is often referred to as [[Real RAM]] model.
 
==Definition==
A BSS machine M is given by the set <math>I</math> of <math>N+1</math> instructions, indexed <math>0, 1, \dots, N</math>. A configuration of M is a tuple <math>(k,r,w,x)</math>, where k is the number of the instruction currently executed, r and w are copy registers and x stores the content of all registers of M. The computation begins with configuration <math>(0,0,0,x)</math> and ends whenever <math>k=N</math>, the final content of x is said to be the output of the machine.
 
The instructions of M can be of the following types:
*Computation<math>(x_{0})</math>: a substitution <math>x_{0} := g_{k}(x)</math> is performed, where <math>g_{k}</math> is an arbitrary rational function; copy registers r and w may be changed, either by <math>r := 0</math> or <math>r := r + 1</math> and similarly for w.  
*Branch<math>(x_{0}, l)</math>: if <math>x_{0} \geq 0</math> then goto l else goto k+1.
*Copy(<math>x_{r}, x_{w}</math>): the content of the "read" register <math>x_{r}</math> is copied into the "write" register <math>x_{w}</math>; the next instruction is k+1
 
==See also==
*[[Hypercomputation]]
*[[Real computer]]
 
==Further reading==
*{{cite book|last=Grädel|first=E.|title=Finite Model Theory and Its Applications|publisher=Springer-Verlag|year=2007|pages=125–230|chapter=Finite Model Theory and Descriptive Complexity|url=http://www.logic.rwth-aachen.de/pub/graedel/FMTbook-Chapter3.pdf}}
*{{cite journal|author=L. Blum, M. Shub, and S. Smale|year=1989|title=On a Theory of Computation and Complexity over the Real Numbers: NP-completeness, Recursive Functions and Universal Machines|journal=Bulletin of the American Mathematical Society|volume=21|issue=1|url=http://www.ams.org/bull/1989-21-01/S0273-0979-1989-15750-9/S0273-0979-1989-15750-9.pdf}}
 
{{DEFAULTSORT:Blum-Shub-Smale machine}}
[[Category:Models of computation]]

Revision as of 01:50, 27 August 2013

In computation theory, the Blum–Shub–Smale machine, or BSS machine, is a model of computation introduced by Lenore Blum, Michael Shub and Stephen Smale, intended to describe computations over the real numbers. Essentially, a BSS machine is a Random Access Machine with registers that can store arbitrary real numbers and that can compute rational functions over reals at unit cost. It is often referred to as Real RAM model.

Definition

A BSS machine M is given by the set I of N+1 instructions, indexed 0,1,,N. A configuration of M is a tuple (k,r,w,x), where k is the number of the instruction currently executed, r and w are copy registers and x stores the content of all registers of M. The computation begins with configuration (0,0,0,x) and ends whenever k=N, the final content of x is said to be the output of the machine.

The instructions of M can be of the following types:

  • Computation(x0): a substitution x0:=gk(x) is performed, where gk is an arbitrary rational function; copy registers r and w may be changed, either by r:=0 or r:=r+1 and similarly for w.
  • Branch(x0,l): if x00 then goto l else goto k+1.
  • Copy(xr,xw): the content of the "read" register xr is copied into the "write" register xw; the next instruction is k+1

See also

Further reading

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