![ The general decision problem of whether a
grammar is ambiguous is undecidable because it
can be shown that it is equivalent to the Post
correspondence problem.[1] At least, there are tools
implementing some semi-decision procedure for
detecting ambiguity of context-free grammars.[2]](https://image.slidesharecdn.com/deterministiccontext-freegrammarsnon-deterministic-150319074305-conversion-gate01/85/Deterministic-context-free-grammars-non-deterministic-13-320.jpg)
Deterministic context free grammars &non-deterministic
- 2. Deterministic context-free grammars are always unambiguous and are an important subclass of unambiguous CFGs; there are non-deterministic unambiguous CFGs, Recognizing ambiguous grammars; Inherently ambiguous languages ... also has the unambiguous grammar, consisting of a single production rule:
- 3. AMBIGUOUS GRAMMAR In computer science, an ambiguous grammar is a context-free grammar for which there exists a string that can have more than one leftmost derivation while an unambiguous grammar is a context-free grammar for which every valid string has a unique leftmost derivation.
- 4. CONTEXT FREE GRAMMAR A context-free language (CFL) is a language accepted by a push-down automaton (PDA). Alternatively, a context-free language is one that has a context-free grammar (CFG) describing it.
- 5. A CFG is a structure (N, Σ, P, S) where N is a set of symbols known as non-terminals, Σ is a set of symbols known as terminals, S ∈ N is called the start symbol, and P is a finite set of production rules. Each production rule is of the form L → R1 R2 . . . Rn, where L ∈ N is a non-terminal and each Ri belongs to N ∪ Σε. We will now present several context-free grammars through examples, and then proceed to examine their properties
- 6. Here is a simple grammar for arithmetic expressions built from numbers out of a given range. Let Σ contain the symbols (, ), +, −, ×, / and the numbers in the desired range, and let N = {S, B}. The production rules are as follows
- 9. A PARSE TREE
- 10. The language generated by a grammar G is the set of all strings α over Σ which are generated by G. 9 Languages generated by context-free grammars are called context-free.
- 11. DETERMINISTIC CONTEXT-FREE GRAMMARS ARE ALWAYS UNAMBIGUOUS,
- 12. RECOGNIZING AMBIGUOUS GRAMMARS OR Non-deterministic
- 13. The general decision problem of whether a grammar is ambiguous is undecidable because it can be shown that it is equivalent to the Post correspondence problem.[1] At least, there are tools implementing some semi-decision procedure for detecting ambiguity of context-free grammars.[2]
- 14. Many languages admit both ambiguous and unambiguous grammars, while some languages admit only ambiguous grammars. Any non-empty language admits an ambiguous grammar by taking an unambiguous grammar and introducing a duplicate rule or synonym (the only language without ambiguous grammars is the empty language). A language that only admits ambiguous grammars is called an inherently ambiguous language, and there are inherently ambiguous context-free languages.
- 15. Thank you