A (*) hierarchy of thesesystems divides them into types 0 through 3.
One type of these systems can be called "proper" if it has no cycles or epsilon productions, in additionto two other requirements. In the conversion from these systems to pushdown automata, the terminal andnonterminal symbols of these systems make up the stack alphabet of the PDA. These systems are formallydefined as a tuple of those symbols as well as production rules and a start symbol. A (*) hierarchy of thesesystems divides them into types 0 through 3. There exist tree-adjoining ones of these, and Backus-Naur Form isused to notate the context-free type of these. A theory about the universal one of these systems states that humanshave the innate ability to learn these systems. For 10 points, name these sets of rules that govern the combination ofwords to form correct phrases in a language.
One type of these systems can be called "proper" if it has no cycles or epsilon productions, in additionto two other requirements.
grammars [or formal grammars; accept contex-free grammars before "types 0" is said; prompt on "languages"]