Alternating 1-based Minsky machine

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An Alternating 1-based Minsky machine (A1MM for short) is pedestrian variation on a Minsky machine which was defined by Chris Pressey in 2024 with the intent of being used as an intermediate language to ease writing Turing-completeness proofs for certain languages. In particular, A1MMs are used in the Strelnokoff Turing-completeness proof.


An Alternating 1-Based Minsky machine is just like a Minsky machine, except

  • Along with the increment and decrement instructions, there is also a NOP instruction. You can think of it being like increment, except instead of adding 1 to the counter, it adds 0. (And of course it is not necessary to identify a particular counter in this case.)
  • The smallest value a counter can take on is 1.
  • The "decrement" instruction tests the counter for being 1 instead of being 0.
  • All counters start with the value 1.
  • All steps must be numbered with integers.
  • Even-numbered steps may only transition to odd-numbered steps, vice-versa. This applies to all transitions out of the step, i.e. both transitions out of a decrement instruction must follow this rule.

Computational class

It should not be difficult to see that every Minsky machine can be converted to an equivalent Minsky machine by:

  • offsetting all values by +1, i.e. anywhere there is a 0 in the Minsky machine, there will be a 1 in the A1MM.
  • rearranging the steps so that all even-number steps transition only to odd-numbered steps and vice versa, inserting extra NOP steps as needed to avoid transitioning to another step of the same parity.

See also