3515ICT Theory of Computation
Tutorial problems: Turing machines, decidability and undecidability
1. Give implementation level and formal descriptions of a Turing machine to recognise the
language
L
=
{
a
n
b
n
c
n

n
≥
0
}
. You may assume either a single or doublyinfinite
tape.
2. Give implementation level and formal descriptions of a Turing machine to compute the
sum of integers
m
and
n
. The input should have the form
1
m
+1
01
n
+1
, with the head on
the leftmost 1, and the output should have the form
1
m
+
n
+1
, with the head again on the
leftmost 1.
3. Give an implementation level description of a Turing machine to compute Ackermann’s
function, defined by
A
(0
, n
) =
n
+ 1
,
A
(
m
+ 1
,
0) =
A
(
m,
1)
,
A
(
m
+ 1
, n
+ 1) =
A
(
m, A
(
m
+ 1
, n
))
. The input and output should have the same form as in the previous
question. (Difficult)
4. (Hopcroft
et al.
, Exercise 8.4.3) Give implementation level descriptions of nondetermin
istic Turing machines — possibly a multitape machines — that recognise the following
languages. Try to exploit nondeterminism to avoid iteration and keep computations short
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 H.F.
 Hopcroft, implementation level

Click to edit the document details