更改

Other authors (Minsky (1967) p. 119, Hopcroft and Ullman (1979) p. 158, Stone (1972) p. 9) adopt a different convention, with new state q_m listed immediately after the scanned symbol S_j:

(定义2): (q_i, S_j, q_m, S_k/E/N, L/R/N)

 

 

: (definition 2): '''(q_i, S_j, q_m, S_k/E/N, L/R/N)'''

 

 

(定义2) : (q < sub > i  ，s < sub > j  ，q < sub > m  ，s < sub > k /E/N，L/R/N)

:: '''(''' current state '''q_i''' ''',''' symbol scanned '''S_j''' ''',''' new state '''q_m''' ''',''' print symbol '''S_k'''/erase '''E'''/none '''N''' ''',''' move_tape_one_square left '''L'''/right '''R'''/none '''N''' ''')'''

:: '''(''' current state '''q_i''' ''',''' symbol scanned '''S_j''' ''',''' new state '''q_m''' ''',''' print symbol '''S_k'''/erase '''E'''/none '''N''' ''',''' move_tape_one_square left '''L'''/right '''R'''/none '''N''' ''')'''

  ( current state q_i , symbol scanned S_j , new state q_m , print symbol S_k/erase E/none N , move_tape_one_square left L/right R/none N )

  ( 当前状态 q_i , 扫描符号 S_j , 新状态 q_m , 打印 S_k/擦除 E/none N , L/right R/none N )

(当前状态 q <sub> i </sub > ，符号扫描 s < sub > j ，新状态 q < sub > m  ，打印符号 s < sub > k /擦除 E/无 n，move _ tape one _ square left L/right R/none n)

其中q_i,是当前状态，S_j是已扫描符号，S_k是打印符号，E是擦除，N是无状态，L是向左移动，R是向右，q_m 是新状态。

For the remainder of this article "definition 1" (the Turing/Davis convention) will be used.

For the remainder of this article "definition 1" (the Turing/Davis convention) will be used.

本文的其余部分将使用“定义1”(Turing/Davis约定)。

本文的其余部分将使用“定义1”(图灵/戴维斯规则)。

|+ Example: state table for the 3-state 2-symbol busy beaver reduced to 5-tuples

例子: 将3状态2符号“繁忙的海狸”简化为5元组

 

{| class="wikitable" style="text-align: center"

{| class="wikitable" style="text-align: center"

|+ Example: state table for the 3-state 2-symbol busy beaver reduced to 5-tuples

|+ 例子: 将3状态2符号“繁忙的海狸”简化为5元组

! Current state

!  

当前状态

当前状态

! Scanned symbol

!  

扫描符号

扫描符号

!

!

! Print symbol

!  

打印符号

打印符号

! Move tape

!  

! Final (i.e. next) state

!  

最终（即下一个）状态

最终（即下一个）状态

! 5-tuples

!  

5元组

5元组

|-

|-

In the following table, Turing's original model allowed only the first three lines that he called N1, N2, N3 (cf. Turing in ''The Undecidable'', p.&nbsp;126). He allowed for erasure of the "scanned square" by naming a 0th symbol S₀ = "erase" or "blank", etc. However, he did not allow for non-printing, so every instruction-line includes "print symbol S_k" or "erase" (cf. footnote 12 in Post (1947), ''The Undecidable'', p.&nbsp;300). The abbreviations are Turing's (''The Undecidable'', p.&nbsp;119). Subsequent to Turing's original paper in 1936–1937, machine-models have allowed all nine possible types of five-tuples:

In the following table, Turing's original model allowed only the first three lines that he called N1, N2, N3 (cf. Turing in ''The Undecidable'', p.&nbsp;126). He allowed for erasure of the "scanned square" by naming a 0th symbol S₀ = "erase" or "blank", etc. However, he did not allow for non-printing, so every instruction-line includes "print symbol S_k" or "erase" (cf. footnote 12 in Post (1947), ''The Undecidable'', p.&nbsp;300). The abbreviations are Turing's (''The Undecidable'', p.&nbsp;119). Subsequent to Turing's original paper in 1936–1937, machine-models have allowed all nine possible types of five-tuples:

In the following table, Turing's original model allowed only the first three lines that he called N1, N2, N3 (cf. Turing in The Undecidable, p.&nbsp;126). He allowed for erasure of the "scanned square" by naming a 0th symbol S₀ = "erase" or "blank", etc. However, he did not allow for non-printing, so every instruction-line includes "print symbol S_k" or "erase" (cf. footnote 12 in Post (1947), The Undecidable, p.&nbsp;300). The abbreviations are Turing's (The Undecidable, p.&nbsp;119). Subsequent to Turing's original paper in 1936–1937, machine-models have allowed all nine possible types of five-tuples:

在下表中，图灵的原始模型只允许前三行，他称之为N1, N2, N3(参见图灵书籍《The Undecidable》p.126）。他允许通过命名第0个S₀="E"或"N"，即“擦除”或者“空白”等。但是，他不允许“不打印”，所以每个指令行都包括“打印符号S_k”或者“擦除E”。这些缩写是图灵在1936-1937年的原始论文之后，机器模型已经允许所有九种可能的五元组类型。

 

在下表中，图灵最初的模型只允许前三行，他称之为 N1，N2，N3。参见图灵在The Undecidable一书中，第126页)。他通过命名第0个符号 s < sub > 0  = “ 擦除”或“ 空白”等，允许擦除“扫描方块”。但是，他不允许不打印，所以每条指令行都包括“打印符号 s < sub > k  ”或“ 擦除”(参见Post（1947），The Undecidable，第300页中的脚注12 ）。这些缩写是图灵的(The Undecidable，第119页)。在图灵于1936-1937年发表原始论文之后，机器模型已经允许所有九种可能的五元组类型:

{| class="wikitable" style="text-align: center"

{| class="wikitable" style="text-align: center"

|-

|-

!

!

! Current m-configuration<br />(Turing state)

!  

当前的m配置<br />(（图灵状态）

! Tape symbol

!  

! Print-operation

!  

打印

打印

! Tape-motion

!  

! Final m-configuration<br />(Turing state)

!  

最终的M配置<br />（图灵状态）

! 5-tuple

!  

5元组

5元组

! 5-tuple comments

!  

5元组注释

5元组注释

! 4-tuple

!  

4元组

4元组

|-

|-

| q_i

| q_i

| S_j

| S_j

| Print(S_k)

| 打印(S_k)

| Left L

| 向左 L

| q_m

| q_m

| (q_i, S_j, S_k, L, q_m)

| (q_i, S_j, S_k, L, q_m)

| q_i

| q_i

| S_j

| S_j

| Print(S_k)

| 打印(S_k)

| Right R

| 向右 R

| q_m

| q_m

| (q_i, S_j, S_k, R, q_m)

| (q_i, S_j, S_k, R, q_m)

| q_i

| q_i

| S_j

| S_j

| Print(S_k)

| 打印(S_k)

| None N

| 空 N

| q_m

| q_m

| (q_i, S_j, S_k, N, q_m)

| (q_i, S_j, S_k, N, q_m)

| q_i

| q_i

| S_j

| S_j

| None N

| 空 N

| Left L

| 向左 L

| q_m

| q_m

| (q_i, S_j, N, L, q_m)

| (q_i, S_j, N, L, q_m)

| q_i

| q_i

| S_j

| S_j

| None N

| 空 N

| Right R

| 向右 R

| q_m

| q_m

| (q_i, S_j, N, R, q_m)

| (q_i, S_j, N, R, q_m)

| q_i

| q_i

| S_j

| S_j

| Erase

| 擦除

| Left L

| 向左 L

| q_m

| q_m

| (q_i, S_j, E, L, q_m)

| (q_i, S_j, E, L, q_m)

| q_i

| q_i

| S_j

| S_j

| Erase

| 擦除

| Right R

| 向右 R

| q_m

| q_m

| (q_i, S_j, E, R, q_m)

| (q_i, S_j, E, R, q_m)

| q_i

| q_i

| S_j

| S_j

| Erase

| 擦除

| None N

| 空 N

| q_m

| q_m

| (q_i, S_j, E, N, q_m)

| (q_i, S_j, E, N, q_m)

Any Turing table (list of instructions) can be constructed from the above nine 5-tuples. For technical reasons, the three non-printing or "N" instructions (4, 5, 6) can usually be dispensed with. For examples see Turing machine examples.

Any Turing table (list of instructions) can be constructed from the above nine 5-tuples. For technical reasons, the three non-printing or "N" instructions (4, 5, 6) can usually be dispensed with. For examples see Turing machine examples.

 

Less frequently the use of 4-tuples are encountered: these represent a further atomization of the Turing instructions (cf. Post (1947), Boolos & Jeffrey (1974, 1999), Davis-Sigal-Weyuker (1994)); also see more at Post–Turing machine.

Less frequently the use of 4-tuples are encountered: these represent a further atomization of the Turing instructions (cf. Post (1947), Boolos & Jeffrey (1974, 1999), Davis-Sigal-Weyuker (1994)); also see more at Post–Turing machine.

较少遇到使用4元组的情况：这些代表了图灵机指令的进一步原子化（参见Post(1947)，Boolos & Jeffrey(1974，1999)，Davis-Sigal-Weyuker(1994)）；也可参见更多的图灵机。

较少遇到使用4元组的情况：这些代表了图灵指令的进一步原子化（参见Post(1947)，Boolos & Jeffrey(1974，1999)，Davis-Sigal-Weyuker(1994)）；

===The "state"===

===The "state"===