Given an alphabet sigma a string constructed from the alphab

Given an alphabet sigma, a string constructed from the alphabet is a concatenation of symbols in that alphabet. Given a string w = w_1w_2 ...w_n where w_i sigma, the reverse of string w, written as w^rev, is the string w in reverse order, i.e., w^rev = w_nw_n-1 ...w_1. For any language A, let A^rev = {w^rev | w A}. Show that if A is regular, so is A^rev.

Solution

a sequence of symbols and characters representing a sring or pattern.matches a set of strings, so regular expressions serve as names for a set of strings. Programming language tokens can be described by regular languages. The specification of regular expressions is an example of a recursive definition.

The various operations on languages are:

Union of two languages L and M is written as

L U M = {s | s is in L or s is in M}

Concatenation of two languages L and M is written as

LM = {st | s is in L and t is in M}

The Kleene Closure of a language L is written as

L* = Zero or more occurrence of language L

etter = [a – z] or [A – Z]

digit = 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 or [0-9]

sign = [ + | - ]