: Write s = xyz with |xy| ≤ p and |y| ≥ 1 . Since |xy| ≤ p , y must be all a s. Let y = a^k, k≥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 .
: Pick s = a^p b^p+1 . Clearly |s| ≥ p .
: 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.
| | Action | |----------|-------------| | 1 | Read Mishra’s theoretical explanation. | | 2 | Attempt 2 easy exercises. | | 3 | Use JFLAP (free software) to simulate your DFA/PDA/TM. | | 4 | If JFLAP rejects, debug. | | 5 | Write final solution with state diagram + transition table. | | 6 | Compare with peer solutions on StackExchange CS . |
: Former TA for Automata Theory, GATE AIR 312. Believes that every CFG has a story to tell.
: Therefore L is not regular.
: Write s = xyz with |xy| ≤ p and |y| ≥ 1 . Since |xy| ≤ p , y must be all a s. Let y = a^k, k≥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 . klp mishra theory of computation full solution
: Pick s = a^p b^p+1 . Clearly |s| ≥ p . : Write s = xyz with |xy| ≤ p and |y| ≥ 1
: 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. JFLAP is the ultimate "solution checker" for Mishra’s
| | Action | |----------|-------------| | 1 | Read Mishra’s theoretical explanation. | | 2 | Attempt 2 easy exercises. | | 3 | Use JFLAP (free software) to simulate your DFA/PDA/TM. | | 4 | If JFLAP rejects, debug. | | 5 | Write final solution with state diagram + transition table. | | 6 | Compare with peer solutions on StackExchange CS . |
: Former TA for Automata Theory, GATE AIR 312. Believes that every CFG has a story to tell.
: Therefore L is not regular.