Yes, it is true that determining whether a given context-free grammar generates a specific language is undecidable.
Chat with our AI personalities
No, not all deterministic finite automata (DFA) are decidable. Some DFAs may lead to undecidable problems or situations.
Regular expressions and context-free grammars are both formal languages used in computer science to describe patterns in strings. Regular expressions are simpler and more limited in their expressive power, while context-free grammars are more complex and can describe a wider range of patterns. Regular expressions can be converted into context-free grammars, but not all context-free grammars can be represented by regular expressions.
Reduction to the halting problem is significant in computational complexity theory because it shows that certain problems are undecidable, meaning there is no algorithm that can solve them in all cases. This has important implications for understanding the limits of computation and the complexity of solving certain problems.
True
True