Processing math: 100%

Context-Free Pumping Lemma

$L = \{a^nb^nc^n \text{: } n \geq 0 \}$

$L = \{ww \text{: } w \in \{a, b\}^*\}$

$L = \{a^nb^ja^nb^j\text{: } n \geq 0, j \geq 0\}$

$L = \{w \in \{a, b, c\}^* \text{: } n_a(w) < n_b(w) < n_c(w)\}$

$L = \{w \in \{a, b, c\}^* \text{: } n_a(w) > n_b(w) = n_c(w)\}$

$L = \{a^ib^jc^k \text{: } i > j, i > k\}$

$L = \{a^nb^n \text{:} n \geq 0\}$

$L = \{a^kb^nc^nd^j \text{: } j \neq k\}$

$L = \{ww_1w^R \text{: } |w_1| \geq 5 \text{, } w \text{ & } w_1 \in \{a, b\}^*\}$

$L = \{ww_1w^R \text{: } |w| = |w_1| \text{, } w \text{ & } w_1 \in \{a, b\}^*\}$

$L = \{w_1b^nw_2 \text{: } n_a(w_1) < n_a(w_2) \text{, } n_a(w_1) < n \text{, } w_1 \text{ & } w_2 \in \{a, b\}^*\}$

$L = \{w_1cw_2cw_3cw_4 \text{: } w_1 = w_2 \text{ or } w_3 = w_4 \text{, } w_i \in \{a, b\}^* \text{, } |w_i| > 0\}$

$L = \{w_1vv^Rw_2 \text{: } n_a(w_1) = n_a(w_2) \text{, } |v| > 3, v, w_1, w_2 \in \{a, b\}^*\}$

1. Select a lemma.
Pick select a lemma L = {(a^n)(b^n)(c^n): n ≥ 0} L = {ww: w ∈ {a, b}*} L = {(a^n)(b^j)(a^n)(b^j): n ≥ 0, b ≥ j} L = {w ∈ {a, b, c}*: n_a(w) < n_b(w) < n_c(w)} L = {w ∈ {a, b, c}*: n_a(w) > n_b(w) = n_c(w)} L = {(a^i)(b^j)(c^k): i > j, i > k} L = {(a^n)(b^n): n ≥ 0} L = {(a^k)(b^n)(c^n)(d^j): j ≠ k} L = {w(w_1)(w^R): |w_1| ≥ 5, w & w_1 ∈ {a, b}*} L = {w(w_1)(w^R): |w| = |w_1|, w & w_1 ∈ {a, b}*} L = {(w_1)(b^n)(w_2): n_a(w_1) < n_a(w_2), n_a(w_1) < n, w_1 & w_2 ∈ {a, b}*} L = {(w_1)c(w_2)c(w_3)c(w_4): w_1 = w_2 or w_3 = w_4, w_i ∈ {a, b}*, |w_i| > 0} L = {(w_1)v(v^R)(w_2): n_a(w_1) = n_a(w_2), |v| > 3, v, w_1, w_2 ∈ {a, b}*}

2. Choose who makes the first move. Press "Enter" to continue.
You go first Computer goes first