Every context-free language is in P; one polynomial-time algorithm taking as input a CFG G and a string x and indicating whether x L(G) is implemented in the simulator; its called the Earley parser if you are curious: https://en.wikipedia.org/wiki/Earley_parser Give a simpler argument that every context-free language is in NP. Do this by showing that for each CFG G, there is a polynomial-time verifier V for L(G). Hint: A string x is generated by a grammar with start symbol S if and only if there exists a derivation S . . . x (or a parse tree with S as the root and x labeling the leaves).

2. Every context-free language is in P; one polynomial-time algorithm taking as input a CFG G and a string x and indicating whether x E L(G) is implemented in the simulator; it's called the Earley parser if you are curious: https://en.wikipedia.org/wiki/Earley-parser Give a simpler argument that every context-free language is in NP. Do this by showing that for each CFG G, there is a polynomial-time verifier V for L(G). Hint: A string z is generated by a grammar with start symbol S if and only if there exists a derivation S (or a parse tree with S as the root and x labeling the leaves). 2. Every context-free language is in P; one polynomial-time algorithm taking as input a CFG G and a string x and indicating whether x E L(G) is implemented in the simulator; it's called the Earley parser if you are curious: https://en.wikipedia.org/wiki/Earley-parser Give a simpler argument that every context-free language is in NP. Do this by showing that for each CFG G, there is a polynomial-time verifier V for L(G). Hint: A string z is generated by a grammar with start symbol S if and only if there exists a derivation S (or a parse tree with S as the root and x labeling the leaves)