#### DMCA

## Bit copying - the ultimate computational simplicity (2009)

Venue: | Complex Systems |

Citations: | 1 - 1 self |

### Citations

14 |
The Ultimate RISC,
- Jones
- 1988
(Show Context)
Citation Context ...o build an imperative language with the smallestspossible numbersofsinstructions,sseveralsonesinstructionssetscomputers(OISC) languages have been invented. One example, the ultimate RISC architectures=-=[1]-=-,sutilizessthessinglesinstructionscopysmemorystosmemory. Complex behavior of such a machine is achieved by mapping the machinesregisterssontosmemoryscells.sForsexample,sasmemoryscellswith the address ... |

10 | Conditional Branching is not Necessary for Universal Computation in von Neumann Computers”,
- Rojas
- 1996
(Show Context)
Citation Context ...r from a simple C-like language has been written to compile programs into Subleq processor code [3]. Attempts to reduce the complexity of the atomic operation have been undertaken. For example, Rojas =-=[4]-=- proves that conditional branching issnotsnecessarysforsuniversalscomputationsgivensthesabilitysofscode self-modification. Complex Systems, 19 © 2011 Complex Systems Publications, Inc. Another example... |

3 | A Very Short Self-Interpreter”,
- Mazonka, Cristofani
- 311
(Show Context)
Citation Context ... presented in this paper has been implemented. Its assembler, emulator, and the library can be downloaded from [7]. Appendix A 4 Only assembly language with a few library macro commands can be regarded exactly as Turing-complete, because they do not have the memory cell size boundary, which limits the address space. Bit copying instructions are loosely Turing-complete or more precisely they are of Linearly Bounded Automaton computational class, which is the class the real computers belong to. Formal proof can be found in [7] where an interpreter of a Turing-complete language DBFI described in [6] is presented. Keymaker (esolangs.org user) argued that the instruction language could be made Turingcomplete if addressing is relative, not absolute. It seems that it is possible to redefine the language to use relative addressing, but that is outside of the scope of this paper.. - 17 - This diagram represents dependencies between functions and macros in the library in the current implementation [7]. Direct dependencies, which are also indirect, are omitted. Different implementation algorithms would result in different dependency diagrams, but general dependency levels would be the same. Appe... |

1 |
Register Machines,” in A New
- Wolfram
(Show Context)
Citation Context ...final result (011), making this entire operation irreversible.s000 001 010 011 100 101 110 111 100 011 011 111 110 100 010 101 Table 1. Asmachine,ssimilarstosregistersmachinessdescribedsbysS.sWolfram =-=[5]-=-, can be realized by using a continuous process of bit inversion on thessamessetsofsbits.sForsexample,sas3-bitsmachinesproducessassequence (000) (100) (110) (010) (011) (111) (101) (100) …. Figures1ss... |

1 |
A Very Short Self-Interpreter.” (Nov 21
- Mazonka, Cristofani
(Show Context)
Citation Context ...nearlysbounded automaton computationalsclass,swhich is the class that real computers belong to. A formal proof can be found ins[6]swheresansinterpretersofsasTuring-completeslanguagesDBFIsdescribedsins=-=[7]-=-sisspresented.sKeymakers(esolangs.orgsuser)sarguedsthat the instruction language could be made Turing-complete if addressing is relative, not absolute. It seems that it is possible to redefine the lan... |

1 |
A New Kinf of Science”,
- Wolfwam
- 2002
(Show Context)
Citation Context ...ersible results if they are used in combination with referencing. In the following table: 000 001 010 011 100 101 110 111 100 011 011 111 110 100 010 101 the first row has initial three bits. The second row has the same bits with one inverted (NOT operation applied). The one inverted is the one referenced by all three, as the index of the bit equal to binary representation taken modulo 3. As one can see two initial states (001 and 010) produce the same final result (011), which makes this entire operation irreversible. A machine, similar to register machines described in Stephen Wolfram’s NKS [4], can be realized using continuous process of bit inversion on the same set of bits. For example, 3 bit machine produce a sequence (000) (100) (110) (010) (011) (111) (101) (100) ... - 3 - The figure above shows Wolfram diagrams for 2, 3, 4, 5, 6, and 7 bit machines. On the right side of each diagram bits represented as dark (for 1) and white (for 0) squares. On the left side a small square shows the interpreted value of the bits – the address of the next bit to be inverted. The address is calculated as the binary representation of some integer taken modulo number of bits. Taking binary value ... |