Turing's (still?) classified inference engine algorithm? Does anyone know the algorithm used by Turing's Colossus inference engine, so highly classified that the Brits kept it secret for decades after WW II?

Indeed, it may still be classified.  Several years ago a colleague of mine, the late Robert Johnson, sent me an email response to my announcement about the Hutter Prize for Lossless Compression of Human Knowledge.  Bob was the guy who designed the Burroughs zero address architecture used for so many years in banking (and incidentally invented magnetic ink used on checks).  He certainly had a lot of background he didn't advertise, including classified work.


  Computerdom does not have a lot of art in inference engines (making
  predictions).  The most effective inference engine that I know of is
  the software done for Colossus, Turing's code breaking "computer" of
  WWII.  The Brits still treat that software as classified even though
  the hardware has been declassified for years.  So far as I know,
  nobody outside of  UK knows the details of that software.  My point
  here is that drawing understanding from natural languages is a
  relatively small art practiced mostly by cryptoanalysts.  And my
  further point is that the natural language of interest (be it English,
  Chinese, Mayan or ...) has a major influence on how one (person or
  program) goes about doing analyses and making inferences.   From a
  practical perspective, the Hutter challenge would be much more
  tractable for at least me if I could do it in Chinese.  My first PhD
  student was Jun Gu who is currently Chief Information Scientist for
  PRC.  His thesis was on efficient compression technologies.   If you
  wish, you can share these thoughts with whomever you please.
  
  Bob Johnson Prof. Emeritus Computer Science Univ. of Utah
This doesn't answer your question, but you may find clues in two wartime papers of Alan Turing which were formerly classified were declassified and published in the UK National Archives in 2015, and are now available on the arXiv:


  Alan M. Turing, ‘The Applications of Probability to Cryptography’, UK National Archives HW 25/37, 1942, arXiv:1505.04714.
  
  Alan M. Turing, ‘Paper on Statistics of Repetitions’, UK National Archives HW 25/38, 1942, arXiv:1505.04715.


It may be possible to reconstruct, from the principles enumerated therein, what algorithm Turing would have implemented in the Colossus to perform the feats it is known to have been able to perform.