* Movement Directions are denoted by R (right) and L (left).
* E is used to denote NULL symbol (or absense of symbol in a tape cell).
* $ denotes a marker ...

Solution Summary

Apart from the transitions list for the turing machine, solution also provides stepwise guidance on how to construct a graphical representation for it.

Let A be a turing-recognizable language consisting of descriptions of Turingmachines, {M1, M2,...}, where every Mi is a decider. Prove that some decidable language D is not decided by any decider Mi whose description appears in A. (Hint: You may find it helpful to consider an enumerator for A.)

Give the transition list for a turingmachine that will determine whether for an input sequence w over symbol set {0,1}, n0(w) = n1(w).
n0(w) and n1(w) respectively indicate the count of 0s and 1s in the word 'w'.

Consider the problem of testing whether a Turingmachine M on an input w ever attempts to move its head left when its head is on the left-most tape cell. Formulate this problem as a language and show that it is undecidable.

Cognitive scientists believe there is an infinite potential variety of human behavior. However, they also believe that this infinite behavior is produced by a finite devise, such as theTuringmachine. How can these two views be reconciled?

For questions 3 to 5, remember that a Turingmachine starts in state 1, reading the leftmost nonblank cell.
1. Given theTuringmachine instruction
(1,1,0,2,L)
and the configuration
... b 1 0 b ... (Tape read head is in state 1, and is over symbol 1 on the left)
Draw the next configuration.
2. A Tur

A Turingmachine with doubly infinite tape is similar to an ordinary Turingmachine except that its tape is infinite to the left as well as to the right. The tape is initially filled with blanks except for the portion that contains the input. Computation is defined as usual except that the head never encounters an end to the t

Please see the attached file for the fully formatted problems.
(a) We wish to design a Turingmachine which, using monadic notation, inputs a
pair (in, n) of positive integers in standard starting position (on an otherwise blank tape), and which halts scanning the rightmost of a string of in is on an otherwise blank tape.
W

Let B be a probabilistic polynomial time Turingmachine and let C be a language where, for some fixed 0 < 1 < 2 < 1,
a. w C implies Pr [B accepts w] 1, and
b. w C implies Pr [B accepts w] 2.
Show that C BPP. HINT:
Use Lemma 10.5 to help you

Construct a turingmachine to compute the product x*y of any two positive integers x and y. Assume that the inputs x and y are represented in unary and are separated by a single 0.