Consider the following rewrite system RRR FF RRF FR a Show t

Consider the following re-write system:

RRR FF RRF FR

(a) Show that each string in { F, R }^* is equivalent to one of the following 6 strings:

, R, RR, F, FR, FRR

(b) (HINTs: Use induction. Is every string of length 2 equivalent to one of the 6 given strings?

If a string w has length n 2, then either w = Rx with length of x = n 1, or w = F x with length of x = n 1.)

(c) Show that a “MODEL” of this system is the set of Triangles with vertices labeled A, B, and C. In this MODEL, how do F and R change the labeling of the vertices of these triangles. (d) Show that there is a mechanical procedure (an algorithm) which determines whether or not two strings in this system are equivalent. (e) Show that there is a Turing nmachine which can determine whether or not two strings in this system are equivalent. (Informal description – do NOT write out instructions.)

(d) Show that there is a mechanical procedure (an algorithm) which determines whether or not two strings in this system are equivalent.

(e) Show that there is a Turing nmachine which can determine whether or not two strings in this system are equivalent. (Informal description – do NOT write out instructions.)

Solution

This question does not belong to algebra.

Sorry, I cannot solve it.