c

1
Alg3 Computability Tutorial Sample Answers
1i
a
a
a
b
a
b
b
b
c
c
c
c
(abc)n anu bnu cn
1ii
a
a
b
b
c
c
1iii Assume unary representation of numbers and
at least one operator.
1
1
1

1


-
-

2

• 2i)
• S0,lt S1,-gt mv to beginning
• S1,0 S2,- delete hd
• S1,1 S2,-
• S1, - H,-
• S2,- S3, -gt mv R
• S3,0 S4,- read ch and blank
• S3,1 S4,-
• S3,- H, -
• S4,- S5,lt- mv L
• S4,- S5,lt-
• S5,- S6,0 write ch
• S5,- S6,1
• S6,0 S7,-gt
• S6,1 S7,-gt mv 2 R
• S7,- S8,-gt
• S8,0 S4,-
• S8,1 S4,- loop
• S8,- H,-

3

• 2iii)
• For every a, write a token onto the tape
• mv L back to lt
• for every b, check there is a token on the tape
  if you run out of tokens, or there are still
  tokens after running out of bs clear tape,
  write 0 and halt.
• mv L back to lt
• for every c, check there is a token on the tape,
  if you run out of tokens, or there are still
  tokens after running out of cs clear tape,
  write 0 and halt.
• clear tape, write 1, and halt.

4

• 3.
• i)HP -gt eHP
• M x converter Me
• Instance of HP instance of eHP
• Define M so that it writes x on its tape and
  then behaves like M.
• ii) HP -gt UHP
• M x converter Ms
• Instance of HP instance of UHP
• Define M so that it clears the input tape,
  writes x on it and then behaves like M.