Question

Suppose L is a regular language with αbet Σ. Give an algorithm to tell whether L:

a) Contains a palindrome
b) Is a context-free language
c) Contains an even number of symbols
d) Is empty

Answer 1

To check different properties of a regular language such as containing a palindrome, being context-free, having an even number of symbols, or being empty, specific algorithms and approaches can be used.

Step-by-step explanation:

a) To determine whether a regular language contains a palindrome, we can construct a finite-state automaton that recognizes the language. If there is a state in the automaton that can transition to itself with any symbol from the alphabet, then the language contains a palindrome.

b) To check if a regular language is context-free, we can convert the regular expression describing the language into an equivalent context-free grammar using the standard conversions. If the converted grammar is context-free, then the language is context-free.

c) To check if a regular language contains an even number of symbols, we can analyze the structure of the regular expression defining the language. If the regular expression has an equal number of opening and closing parentheses or square brackets, then the language contains an even number of symbols.

d) To determine if a regular language is empty, we can construct a finite-state automaton that recognizes the language. If the automaton has no accepting states, then the language is empty.