Consider the grammar shown below.S → C CC → c C | dThe gra...
Since there is no conflict, the grammar is LL(1). We can construct a predictive parse table with no conflicts. This grammar also LR(0), SLR(1), CLR(1) and LALR(1).
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Consider the grammar shown below.S → C CC → c C | dThe gra...
Context-Free Grammar:
A context-free grammar (CFG) is a set of production rules that define the structure of strings in a formal language. It consists of a set of non-terminal symbols, a set of terminal symbols, a start symbol, and a set of production rules.
LL(1) Grammar:
An LL(1) grammar is a context-free grammar that can be parsed using a top-down parser with a single token lookahead. The LL(1) property means that for any pair of distinct productions for a non-terminal symbol, there must be a unique terminal symbol that can be used to differentiate between them.
SLR(1) Grammar:
An SLR(1) grammar is a context-free grammar that can be parsed using a bottom-up parser called the SLR(1) parser. The SLR(1) property means that for any state in the parser, there must be a unique lookahead symbol that can be used to determine the next action.
LALR(1) Grammar:
An LALR(1) grammar is a context-free grammar that can be parsed using an LALR(1) parser. LALR(1) parsers are a type of bottom-up parser that are more powerful than SLR(1) parsers. LALR(1) grammars can handle a larger class of context-free languages than SLR(1) grammars.
LR(1) Grammar:
An LR(1) grammar is a context-free grammar that can be parsed using an LR(1) parser. LR(1) parsers are a type of bottom-up parser that are more powerful than LALR(1) parsers. LR(1) grammars can handle a larger class of context-free languages than LALR(1) grammars.
Analysis of the Given Grammar:
Let's analyze the given grammar to determine its properties:
S → C CC | c C | d
- The start symbol is 'S'.
- The non-terminal symbols are 'S', 'C', and 'CC'.
- The terminal symbols are 'c' and 'd'.
- The production rules are:
1. S → C CC
2. S → c C
3. S → d
LL(1) Analysis:
To determine if the grammar is LL(1), we need to check if there is a unique terminal symbol for each pair of distinct productions for a non-terminal symbol.
- For the non-terminal symbol 'S', we have three distinct productions.
- S → C CC
- S → c C
- S → d
There is no unique terminal symbol that can be used to differentiate between these productions, as 'C' and 'c' can both be the first symbol.
Therefore, the grammar is not LL(1).
SLR(1) Analysis:
To determine if the grammar is SLR(1), we need to check if there is a unique lookahead symbol for each state in the parser.
- We can construct the SLR(1) parsing table for the grammar, but it may not be feasible to explain it in detail here.
- However, we can observe that the grammar has reduce-reduce conflicts, which means that there are states in the parser where