Undecidable Problems
Some questions that are undecidable for wider classes of grammars become decidable for context-free grammars; e.g. the emptiness problem (whether the grammar generates any terminal strings at all), is undecidable for context-sensitive grammars, but decidable for context-free grammars.
Still, many problems remain undecidable. Examples:
Read more about this topic: Context-free Grammar
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“What we know, is a point to what we do not know. Open any recent journal of science, and weigh the problems suggested concerning Light, Heat, Electricity, Magnetism, Physiology, Geology, and judge whether the interest of natural science is likely to be soon exhausted.”
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