Statement: LR(1) parsing is sufficient for deterministic context-free languages.

Explanation:
To understand the given statement, let's first discuss some concepts related to parsing and context-free languages.

Context-Free Languages:
A context-free language is a language that can be generated by a context-free grammar. A context-free grammar is a set of production rules that define the structure of valid strings in the language.

LR(1) Parsing:
LR(1) parsing is a bottom-up parsing technique based on the construction of LR(1) parsing tables. An LR(1) parser uses a stack to keep track of the parsing process and a parsing table to determine the next action based on the current state and lookahead symbol.

Deterministic Context-Free Languages:
A context-free language is said to be deterministic if there is at most one valid parse tree for each string in the language. In other words, there are no ambiguities or conflicts in the parsing process.

Explanation of the Statement:
The given statement claims that LR(1) parsing is sufficient for deterministic context-free languages. This means that if a language is deterministic, an LR(1) parser can always parse it without any conflicts or ambiguities.

Proof:
To prove the statement, we need to show that for any deterministic context-free language, an LR(1) parser can be constructed without any reduce-reduce or shift-reduce conflicts.

Shift-Reduce Conflicts:
A shift-reduce conflict occurs when the parser encounters a state where it can either shift the next input symbol onto the stack or reduce the current stack symbols to a non-terminal. This conflict arises due to the ambiguity in the parsing process.

Reduce-Reduce Conflicts:
A reduce-reduce conflict occurs when the parser encounters a state where it can reduce the current stack symbols to multiple non-terminals. This conflict also arises due to the ambiguity in the parsing process.

LR(1) Parsing Tables:
LR(1) parsing tables are constructed based on LR(1) items, which are augmented versions of the production rules in the grammar. LR(1) items contain information about the current state, the next input symbol, and the possible actions (shift, reduce, or accept).

LALR(1) Parsing:
LALR(1) parsing is a variation of LR(1) parsing where the parser tables are compressed to reduce the memory requirements. LALR(1) parsers can handle a larger class of grammars compared to LR(1) parsers.

Proof by Contradiction:
Assume that an LR(1) parser for a grammar G does not have any reduce-reduce conflict. This means that the LR(1) parsing tables are conflict-free and unambiguous. If the LR(1) parser can parse G without any conflicts, then it implies that the grammar G is a deterministic context-free language.

Therefore, the given statement is true. LR(1) parsing is sufficient for deterministic context-free languages.

Conclusion:
The given statement is true. LR(1) parsing is sufficient for deterministic context-free languages. This means that if a language is deterministic, an LR(1) parser can always parse it without any conflicts or ambiguities.