圖靈機設計0和1

Question

f1（1 ^ n01 ^ m）= 1 ^ | mn |

設計可計算功能的圖靈機（轉換圖）

如何跟蹤中間的0？ 我已經嘗試過但無法解決

Answer 1

我假設您希望磁帶字母僅包含0、1和-（空白）。 在使用單帶圖靈機時，我們的策略是富有成效的策略：我們將在中間的0左右來回彈跳，找到它們就越過1。 我們將繼續操作，直到用完1秒並達到空白。 此時，磁帶上剩余的全部為1 ^ | mn |。 以及n + m + 1- | mn | 零。 最后，我們將結果復制到磁帶的開頭（如果尚未到達該位置，即m> n），然后擦除零。

Q    s    s'   D    Q'

// read past 1^n
q0   1    1    R    q0

// read through zeroes
q0   0    0    R    q1
q1   0    0    R    q1

// mark out the first 1 remaining in 1^m
q1   1    0    L    q2

// read through zeros backwards
q2   0    0    L    q2

// mark out the last 1 remaining in 1^n
q2   1    0    R    q1

// we were reading through zeroes forward
// and didn't find another 1. n >= m and
// we have deleted the same number from
// the first and last parts so just delete
// zeroes
q1   -    -    L    q3
q3   0    -    L    q3
q3   1    1    L    halt_accept

// we were reading through zeroes backwards
// and didn't find another 1. n < m and we
// accidentally deleted one too many symbols
// from the 1^m part. write it back and start
// copying the 1s from after the 0s back to
// the beginning of the tape. then, clear zeroes.
q2   -    -    R    q4
q4   0    1    R    q5
q5   0    0    R    q5
q5   1    0    L    q6
q6   0    0    L    q6
q6   1    1    R    q4
q5   -    -    L    q7
q7   0    -    L    q7
q7   1    1    L    halt_accept

自然，沒有TM示例的執行就不會完整。

-111110111-   =>   -111110111-   =>   -111110111-
 ^                   ^                   ^
 q0                  q0                  q0

=>   -111110111-   =>   -111110111-   =>   -111110111-
         ^                   ^                   ^
         q0                  q0                  q0

=>   -111110111-   =>   -111110011-   =>   -111110011-
            ^                 ^                 ^
            q1                q2                q2

=>   -111100011-   =>   -111100011-   =>   -111100011-
           ^                   ^                   ^
           q1                  q1                  q1

=>   -111100001-   =>   -111100001-   =>   -111100001-
            ^                 ^                 ^
            q2                q2                q2

=>   -111100001-   =>   -111000001-   =>   -111000001-
         ^                   ^                   ^
         q1                  q1                  q1

=>   -111000001-   =>   -111000001-   =>   -111000001-
            ^                   ^                   ^
            q1                  q1                  q1

=>   -111000000-   =>   -111000000-   =>   -111000000-
             ^                 ^                 ^
            q2                 q2                q2

=>   -111000000-   =>   -111000000-   =>   -111000000-
          ^                 ^                 ^
          q2                 q2                q2

=>   -110000000-   =>   -110000000-   =>   -110000000-
         ^                   ^                   ^
         q1                  q1                  q1

=>   -110000000-   =>   -110000000-   =>   -110000000-
            ^                   ^                   ^
            q1                  q1                  q1

=>   -110000000-   =>   -110000000-   =>   -11000000--
               ^                 ^                 ^
               q1                q3                q3

=>   -1100000---   =>   -110000----   =>   -11000-----
            ^                 ^                 ^
            q1                q3                q3

=>   -1100------   =>   -110-------   =>   -11--------
         ^                 ^                 ^
         q1                q3                q3

=>   -11--------
      ^ 
      halt_accept