Question

1. Construct pushdown automata (deterministic or nondeterministic) that accept the following languages. Provide a brief English description of how your PDA works, as well as a state diagram for the PDA. [Reminder: The model that we used for a PDA is significantly different from the one in the book. Please review the lecture slides and your notes from class.] (a) $L_1 = \{w \in \{0,1,2\}^* \mid n_0(w) + n_1(w) \ge n_2(w)\}$ where $n_0(w)$ represents the number of zeroes in w, $n_1(w)$ represents the number of ones, and $n_2(w)$ represents the number of twos. (Hint: You should be able to do this with just two states.) (b) $L_2 = \{0^m1^n2^q \mid m, n, q \in \mathbb{Z}, m \ge 1, n \ge 0, q > n\}$ (For example, the strings 0011222, 0000012222 and 02 are in $L_2$. The strings 012, 0001112, 122 and $\epsilon$ are not.)

          1. Construct pushdown automata (deterministic or nondeterministic) that accept the following
languages. Provide a brief English description of how your PDA works, as well as a state diagram
for the PDA.
[Reminder: The model that we used for a PDA is significantly different from the one in the
book. Please review the lecture slides and your notes from class.]
(a) $L_1 = \{w \in \{0,1,2\}^* \mid n_0(w) + n_1(w) \ge n_2(w)\}$
where $n_0(w)$ represents the number of zeroes in w, $n_1(w)$ represents the number of ones,
and $n_2(w)$ represents the number of twos. (Hint: You should be able to do this with
just two states.)
(b) $L_2 = \{0^m1^n2^q \mid m, n, q \in \mathbb{Z}, m \ge 1, n \ge 0, q > n\}$ 
(For example, the strings 0011222, 0000012222 and 02 are in $L_2$. The strings 012,
0001112, 122 and $\epsilon$ are not.)

$1. Construct pushdown automata (deterministic or nondeterministic) that accept the following languages. Provide a brief English description of how your PDA works, as well as a state diagram for the PDA. [Reminder: The model that we used for a PDA is significantly different from the one in the book. Please review the lecture slides and your notes from class.] (a) L1 = {w ∈{0,1,2}^* | n0(w) + n1(w) ≥ n2(w)} where n0(w) represents the number of zeroes in w, n1(w) represents the number of ones, and n2(w) represents the number of twos. (Hint: You should be able to do this with just two states.) (b) L2 = {0^m1^n2^q | m, n, q ∈ℤ, m ≥ 1, n ≥ 0, q > n} (For example, the strings 0011222, 0000012222 and 02 are in L2. The strings 012, 0001112, 122 and ϵ are not.)$

Added by Sergio P.

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