[seqfan] Inductive Inference approach for integer sequences

[Alexander P-sky]

1,
Inductive Inference of Integer Sequences
File Format: PDF/Adobe Acrobat -
by S Tetruashvili - 2010 -
In this senior thesis we will exploring the inductive inference of
integer sequences. For example, consider the first few terms of the
Fibonacci sequence ...
www.cs.cmu.edu/afs/cs/user/mjs/ftp/thesis-program/.../tetruashvili.pdf
2.
Computational support for discrete mathematics: DIMACS workshop, ... -
Nathaniel Dean, Gregory E. Shannon, DIMACS (Group) - 1994 -
Mathematics - 399 pages
Integer sequence analysis can be viewed as a problem in inductive
inference, and Angluin and Smith provide an excellent survey of this
field [4]. ...
books.google.com/books?isbn=0821866052...
3.
CiteULike: Inductive inference: A recursion theoretic approach
by L Blum - Cited by 11 -
What an inductive inference machine does is to request and obtain data
in the ... a finite sequence of integers and asked to produce the next
integer in the ...
www.citeulike.org/user/hubris/article/7894876
==================================
On 2/12/11, Alexander P-sky <apovolot at gmail.com> wrote:
> Perhaps the late Ray Solomonoff's Inductive Inference approach could help ?
>
> http://en.wikipedia.org/wiki/Ray_Solomonoff
>
> ARP
> ==============================
> On 2/12/11, Simon Plouffe <simon.plouffe at gmail.com> wrote:
>> Hello,
>>
>>  I am compiling a new set of formulas that
>> are automatically generated from my set of
>> programs and I have 1 idea that could be useful.
>>
>>  There is a way to get a measure of the validity of
>> a conjectural formula, there are 3 pieces of information
>> we can use :
>>
>> 1) The number of known terms in the sequence.
>> 2) The length in characters of the sequence.
>> 3) The length of the supposed formula.
>>
>> measure = log(number of terms)*length(sequence)/length(formula).
>>
>> This gives a number from 0 to ...
>>  a value of < 4 is usualy suspect.
>> a value of 20 or more says that given the number of terms,
>> the length of the formula, this result can be considered quite good,
>>
>> I am presently re-calculating all the formulas obtained so far and
>> the measure is quite precise.
>> So I propose to include this result in my list of formulas I have so
>> far, for the moment I will REJECT all formulas with a score of less
>> than 4 and look carefuly to the ones in between 4 and let's say 20
>> or more. The key measure is in fact the ratio between
>> length(sequence)/length(formula) the log part is to add a weight
>> , if a sequence contains only 6 terms then the confidence is low,
>> if the sequence contains 100 + terms then it add to the value
>> or score.
>>
>>  if someone has a suggestion ? a more precise measure or
>> score, please let me know,
>>
>> ps : I took the list of names from a recent post of mr Lebrun, please
>> could you forward this mail to other members of the sequence list
>> or the editor board ?
>>
>>  best regards,
>>  Simon Plouffe
>>
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>>
>