From: Thomas Walker Lynch Date: Fri, 17 Jul 2026 18:07:47 +0000 (+0000) Subject: TTCA machine definition X-Git-Url: https://git.reasoningtechnology.com/%27%20%20%20window.RT.dirpr_library%20%20%20%27/Hindu-Arabic%20number%20fig%201.png?a=commitdiff_plain;h=814fd80d6d33f2d73d9094f8a46a8d5ed5d1f637;p=TM-2026 TTCA machine definition --- diff --git a/document/book/TM-2026.html b/document/book/TM-2026.html index 683fc38..4fe27d1 100644 --- a/document/book/TM-2026.html +++ b/document/book/TM-2026.html @@ -513,24 +513,23 @@

The following modifications will be made to the computation theoretic Turing Machine definition so as to support the unspecified symbol:

  1. Move to a Moore style programmed state controller, so that actions can be managed separately from state transitions.
    2. -
  2. Introduce explicit actions for reading: a state transition gating read (read_g) and a data read (read_d), which target their respective dedicated registers. Additionally, provide a status action that also targets a dedicated register.
    3. +
  3. Introduce explicit actions for reading: a state transition gating read (read_g) and a data read (read_d), which target their respective dedicated registers. Additionally, provide a status action that also targets the g register.
  4. To match the read functions, the write actions can specify writing a constant symbol (write_σ), or the contents of either the data or gate register (write_d, write_g).
  5. If the unspecified symbol is read into the state transition gating register, the machine transitions to the predefined unspecified_decision state.
-

For ease of programming, the new machine evaluates next-state transitions through a strict four-layer hierarchy:

+

For ease of programming, the new machine evaluates next-state transitions through a four-layer hierarchy:

    -
  1. Fixed Hardware Trap (δF_0): A global interrupt. If the gate register holds the unspecified symbol, the machine unconditionally traps to the unspecified_decision state.
    2. -
  2. Programmed Conditional (δ_1): Evaluates the current state alongside the contents of a targeted read register (either data or gate) to determine the next state.
    3. -
  3. Programmed Default (δ_2): If no register-specific condition is met, this layer provides a default destination state based solely on the current state, ignoring register contents.
    4. +
  4. Fixed global default (δF_0): Selects the rule that matches the value in the gate register. There is only one rule in this set; it compares the gate register to the unspecified symbol, then transitions to the unspecified_decision state.
    5. +
  5. Programmed Conditional (δ_1): Selects the transition rule that matches the current state and the value of the gate register.
    6. +
  6. Programmed Default (δ_2): If no programmed conditional next state rule is found, selects the default transition rule that matches the current state.
  7. Global Fallback (δ_3): An unconditional transition of last resort if no prior layer provides a valid next state.
-

For clarity of presentation, the definition will be partitioned according to separation of concerns. The first section defines the fixed hardware components that dictate universal Turing Machine behavior. The second section defines the memory elements (variables). The third section describes the programmable components, which vary between specific Turing Machines depending on their purposes.

+

For clarity of presentation, the definition will be partitioned according to separation of concerns. The first section defines the fixed parts of the Turing Machine definition. The second section defines the memory elements (variables). The third section describes the programmable components, which vary between specific Turing Machines depending on their purposes.

There is a mechanical procedure for converting a Moore Machine into a Mealy Machine, and the reverse. Two such converted machines are equally expressive. Making the read operation an explicit action, instead of having it implied by a state transition, increases the number of states in a controller, and consequently the number of steps that must be taken. However, the new machine can do in two steps anything the former machine could do in one; consequently, this change affects the multiplier constant on the linear term of the step count formula but does not change the computation complexity class determined from such a step count. The layers of next-state functions can be collapsed into one layer, where the missing arguments are filled in with all possible unused values. This potentially increases the number of state transition arcs that must be specified, but the state transition logic and the number of states remain unchanged. Partitioning the machine definition by separation of concerns does not change the total specification. Hence, these modifications are computationally inconsequential.

-

The TTCA Turing Machine fixed part