Answered step by step
Verified Expert Solution
Question
1 Approved Answer
Define a language S containing words over the alphabet = {a, b} inductively in the following way: The empty word is in S : S
Define a language S containing words over the alphabet = {a, b} inductively in the following way:
-
The empty word is in S: S.
-
If u, v S, then auavb S.
-
If u, v, w S, then buavaw S.
-
Question: Use induction to prove that w S. #a(w) = 2 #b(w).
-
Hint: You might want to show that #a(auavb)=2+#a(u)+#a(v). How do you prove this? This property follows from a lemma that you can perhaps prove by induction: u,v*.#a(uv)=#a(u)+#a(v).
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started