Copy and complete the table below, according to the original Chomsky hierarchy for exhibiting the relationship between grammars. The table should contain the following: Type, Name... Copy and complete the table below, according to the original Chomsky hierarchy for exhibiting the relationship between grammars. The table should contain the following: Type, Name of language Generated, Production Restrictions A -> B, and Acceptor.
Understand the Problem
The question is asking to complete a table about the Chomsky hierarchy. The table needs to include the type of grammar, the name of the language generated by that type, the production restrictions, and the acceptor (automaton) that recognizes the language.
Answer
Here is the completed Chomsky Hierarchy table: Type 0: Recursively Enumerable, None, Turing Machine. Type 1: Context-Sensitive, A ->= 1, Linear-Bounded Automaton. Type 2: Context-Free, A -> α, Pushdown Automaton. Type 3: Regular, A -> aB or A -> a, Finite State Automaton.
Here is the completed table according to the Chomsky Hierarchy:
| Type | Name of language Generated | Production Restrictions A → B | Acceptor |
|---|---|---|---|
| 0 | Recursively Enumerable | None | Turing Machine |
| 1 | Context-Sensitive | A 1 | Linear-Bounded Automaton |
| 2 | Context-Free | A → α, A ∈ N, α ∈ (N ∪ T)* | Pushdown Automaton |
| 3 | Regular | A → aB or A → a, A, B ∈ N, a ∈ T | Finite State Automaton |
Answer for screen readers
Here is the completed table according to the Chomsky Hierarchy:
| Type | Name of language Generated | Production Restrictions A → B | Acceptor |
|---|---|---|---|
| 0 | Recursively Enumerable | None | Turing Machine |
| 1 | Context-Sensitive | A 1 | Linear-Bounded Automaton |
| 2 | Context-Free | A → α, A ∈ N, α ∈ (N ∪ T)* | Pushdown Automaton |
| 3 | Regular | A → aB or A → a, A, B ∈ N, a ∈ T | Finite State Automaton |
More Information
The Chomsky hierarchy is a containment hierarchy, meaning each level includes all the levels below it. Type 0 is the most general, and Type 3 is the most restrictive.
Tips
A common mistake is confusing the order of the types or the corresponding automata. Remember the order: Recursively Enumerable, Context-Sensitive, Context-Free, Regular. Also, remember the corresponding automata: Turing Machine, Linear-Bounded Automaton, Pushdown Automaton, Finite State Automaton.
Sources
- Chomsky Hierarchy in Theory of Computation - GeeksforGeeks - geeksforgeeks.org
- Chomsky hierarchy - Wikipedia - en.wikipedia.org
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