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Counter Machines

In this video I introduce counter machines/register machines, a mathematical model of computation that's Turing complete, and in some circumstances can be easier to work with than Turing machines. You can read about the process of updating line numbers when relocating code here: https://en.wikipedia.org/wiki/Relocat...) You may already be familiar with a lot of tricks for working with counter machines if you've tried my FRACTRAN interactive. The interactive is at https://trkern.itch.io/fractran . I also have a walkthrough that goes through all the tricks you need for programming in FRACTRAN:    • FRACTRAN Walkthrough and Strategy Guide   Computerphile has a video about counter machines that goes into more detail about implementing division and Turing machines:    • Turing Machine Alternative (Counter Machin...   . My state transition diagram notation is based on the notation in this video to hopefully make it more clear. You can also find proofs of Turing Completeness in Minsky's: -"Recursive Unsolvability of Post's Problem of 'Tag' and Other Topics in Theory of Turing Machines" (1961) -"Computation: Finite and Infinite Machines" (1967) You can find lists of variants of counter machines on wikipedia: https://en.wikipedia.org/wiki/Counter... https://en.wikipedia.org/wiki/Counter...