Consider the following statements. $S_1$ : Every SLR(1) grammar is unambiguous but there are certain unambiguous grammars that are not SLR(1). $S_2$ : For any context-free grammar, there is a parser that takes at most $O(n^3)$ time to parse a string of length $n$. Which one of the following options is correct?

Let us analyze both statements:

1. Statement $S_1$:

   • All $\text{LR}(k)$ grammars (including $\text{SLR}(1)$) are deterministic and therefore unambiguous.

   • However, the class of $\text{SLR}(1)$ grammars is a strict subset of unambiguous context-free grammars (for instance, $\text{LR}(1)$ or $\text{LALR}(1)$ grammars that are not $\text{SLR}(1)$, as well as unambiguous grammars that are not deterministic). Thus, there are unambiguous grammars that are not $\text{SLR}(1)$.

   • Therefore, $S_1$ is true.

2. Statement $S_2$:

   • General context-free parsing algorithms such as the CYK (Cocke-Younger-Kasami) algorithm or Earley's parser can parse any arbitrary context-free grammar for a string of length $n$ in at most $O(n^3)$ worst-case time.

   • Therefore, $S_2$ is true.

Since both $S_1$ and $S_2$ are true, option (C) is the correct choice.