Exercises on push-down automata (PDA)

  1. Deterministic uniquely-accepting PDA for {anbnn0}\{ a^n b^n \mid n\geq 0 \}
  2. Deterministic uniquely-accepting PDA for {a2nbnn0}\{ a^{2n} b^n \mid n\geq 0 \}
  3. Deterministic uniquely-accepting PDA for {w{a,b}wa=wb}\{ w \in \{a,b\}^* \mid |w|_a=|w|_b \}
  4. Deterministic uniquely-accepting PDA for {w{a,b}wawb}\{ w \in \{a,b\}^* \mid |w|_a\neq|w|_b \}
  5. Deterministic uniquely-accepting PDA for {w{a,b}wawb}\{ w \in \{a,b\}^* \mid |w|_a\geq|w|_b \}
  6. Deterministic uniquely-accepting PDA for {w{a,b}2wa=wb}\{ w \in \{a,b\}^* \mid 2|w|_a=|w|_b \}
  7. Deterministic uniquely-accepting PDA for {w{a,b}2wawb}\{ w \in \{a,b\}^* \mid 2|w|_a\geq|w|_b \}
  8. Deterministic uniquely-accepting PDA for {w{a,b}2wawb}\{ w \in \{a,b\}^* \mid 2|w|_a\leq|w|_b \}
  9. Uniquely-accepting PDA for {aibjji2j}\{ a^i b^j \mid j\leq i\leq 2j \}
  10. Deterministic uniquely-accepting PDA for {w{a,b}waa=wb}\{ w \in \{a,b\}^* \mid |w|_{aa}=|w|_b \}
  11. Deterministic uniquely-accepting PDA for {aibjcki=j+k}\{ a^i b^j c^k \mid i=j+k \}
  12. Deterministic uniquely-accepting PDA for {aibjckj=i+k}\{ a^i b^j c^k \mid j=i+k \}
  13. PDA for {aibjcki=ji=k}\{ a^i b^j c^k \mid i=j \vee i=k \}
  14. PDA for {aibjcki=jj=k}\{ a^i b^j c^k \mid i=j \vee j=k \}
  15. Uniquely-accepting PDA for {aibjckdi=j}{aibjckej=k}\{ a^i b^j c^k d \mid i=j \} \cup \{a^i b^j c^k e\mid j=k \}
  16. Uniquely-accepting PDA for {w{a,b}w=wR}\{ w \in \{a,b\}^* \mid w=w^R \}
  17. Deterministic uniquely-accepting PDA for the well-parenthesized words over {(,)}\{ ( , ) \}
  18. Deterministic uniquely-accepting PDA for the well-parenthesized words over {[,],(,)}\{ [ , ] , ( , ) \}
  19. Deterministic uniquely-accepting PDA for {xcyx,y{a,b}xa=yb}\{ xcy \mid x,y\in\{a,b\}^* \wedge |x|_{a}=|y|_{b} \}
  20. Deterministic uniquely-accepting PDA for {xcyx,y{a,b}xab=yba}\{ xcy \mid x,y\in\{a,b\}^* \wedge |x|_{ab}=|y|_{ba} \}
  21. Deterministic uniquely-accepting PDA for {xcyx,y{a,b}xaba=ybab}\{ xcy \mid x,y\in\{a,b\}^* \wedge |x|_{aba}=|y|_{bab} \}