{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# hw1 - CSCI 2400 Models of Computation Homework 1 Solutions...

This preview shows pages 1–2. Sign up to view the full content.

CSCI 2400 - Models of Computation Homework 1 Solutions Problem 1 (25 points) Prove that if A and B are languages over the same alphabet Σ and A B , then A * B * . Solution: We will prove by mathematical induction that A k B k , for all k 0. Base case: A 0 B 0 ⇒ { λ } ⊆ { λ } Inductive hypothesis: Assume that A k B k for some k 0. Inductive step: Given that A k B k , demonstrate that A k +1 B k +1 : A k B k A k · A B k · A B k · B A k +1 B k +1 Thus, we can show that A k B k for any positive, Fnite k by building up from our base case, one step at a time. It follows that because A * = A 0 A 1 . . . and B * = B 0 B 1 . . . , then A * B * . Problem 2 (25 points) Prove that there does not exist a language L such that: L * = { a } * { b } * . Solution: Assume that there is such a language, and attempt to Fnd a contra- diction. { a

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

hw1 - CSCI 2400 Models of Computation Homework 1 Solutions...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online