

6. Use the construction in Theorem 4.1 to find nfa's that accept (a) L ((ab) "a)...
Find nfa’s that accept (a) L ((ab)∗ a∗) ∩ L (baa∗) (b) L (ab∗a∗) ∩ L (a∗b∗a) Could someone show me how to construct these and explain their reasoning at each step? Thanks!
dn 6. Use the theorem, L {t" f(t)} = (-1)" den! F(s), to find each of the following: (a) L {t cos 2t} (b) L {t sint}
3 > . No credit for 5. Use the Convolution Theorem to find L any other method. (10 points)
THEOREM 3.1 Let r be a regular expression. Then there exists some nondeteministic finite accepter that accepts L (r) Consequently, L () is a regular language. Proof: We begin with automata that accept the languages for the simple regular expressions ø, 2, and a E . These are shown in Figure 3.1(a), (b), and (c), respectively. Assume now that we have automata M (r) and M (r) that accept languages denoted by regular expressions ri and r respectively. We need...
9. Use the construction in the proof of the Chinese remainder theorem to find a solution to the system of congruences X 1 mod 2 x 2 mod 3 x 3 mod 5 x 4 mod 11 10. Use Fermats little theorem to find 712 mod 13 11. What sequence of pseudorandom numbers is generated using the linear congruential generator Xn+1 (4xn + 1) mod 7 with seed xo 3?
9. Use the construction in the proof of the Chinese...
1. Use the construction of Theorem 2.2 to convert the nfa in Figure 2.10 to a dfa. Can you see a simpler answer more directly?
1. Construct a DFSM to accept the language: L w E ab): w contains at least 3 as and no more than 3 bs) 2. Let E (acgt and let L be the language of strings consisting of repeated copies of the pairs at, ta, cg. ge. Construct both a DFSM to accept the language and a regular expression that represents the language. 3. Let ab. For a string w E , let w denote the string w with the...
6. Use the power theorem to find the value of the following integr sinc Answer:
Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = 282 - 4 sin(56) L{f(t)}
Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = (2t - 1)3 %3D L{f(t)} =