What is the Church or Turing thesis?

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What is the Church or Turing thesis?..

Answer / aki

Sorry for not explaining well.
got from :
http://www.cmi.ac.in/~ramprasad/lecturenotes/algcomp/lecture20.pdf

Turing and Church had considered various computational
models, such as
Turing machines, random-access machines, and so on. All
these computational
models could be implemented through physical systems subject to
the laws of classical mechanics. While studying many such
computational
models, computer scientists came up with the following Holy
Grails:
1
1. Church-Turing thesis: This states that any computational
model
is as powerful as the Turing machine. In other words, given
any computational
model, we can simulate computations on that model using
the Turing machine. The simulation may of course involve a
blow-up
in time taken as well as in space used.
2. Strong Church-Turing thesis: This states that for any
computational
model, a polynomial-time algorithm for a decision problem in
that computational model can be simulated by a
polynomial-time algorithm
in the Turing machine model. In looser language, if we think
of polynomial time as the notion of tractability, then
tractability in
any computational model is equivalent to tractability in the
Turing
machine model.
3. Strong Church-Turing thesis (randomized version): This states
that for any computational model, a bounded-error
probabilistic polynomial
time algorithm for a decision problem in that computational
model can be simulated by a bounded-error probabilistic
polynomial
time algorithm for the problem in the Turing machine model.
In looser
language, if we think of BPP as the notion of tractability,
then BPP
is any computational model is equivalent to tractability in
the Turing
machine model.

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