: Pump up: xy^2 z = a^p+k b^p+1 . Now p+k ≥ p+1 (since k≥1), so p+k is NOT less than p+1 . Hence xy^2 z ∉ L . Contradiction.
: Pick s = a^p b^p+1 . Clearly |s| ≥ p . klp mishra theory of computation full solution
However, the book is notorious for two things: and cryptic exercises . Students often search for the mythical "KLP Mishra full solution" to crack the code of Finite Automata, Pushdown Automata, and Turing Machines. : Pump up: xy^2 z = a^p+k b^p+1
JFLAP is the ultimate "solution checker" for Mishra’s automata problems. It will literally draw the DFA for you. Yes. While formal languages are mature, Mishra’s problem set is unmatched for GATE and PhD entrance exams. The "full solution" is not a document – it is a skill . Contradiction
: Write s = xyz with |xy| ≤ p and |y| ≥ 1 . Since |xy| ≤ p , y must be all a s. Let y = a^k, k≥1 .