A language accepted by Deterministic Push down automata is closed unde...
Deterministic Pushdown Automata
A deterministic pushdown automaton (DPDA) is a type of automaton that is used to recognize languages generated by context-free grammars. It is similar to a deterministic finite automaton (DFA), but with an added stack that allows it to handle context-free languages.
Closure Properties of Languages
Closure properties of languages refer to the properties that are preserved under certain operations on languages. For example, if a language L is closed under the complement operation, it means that if L is a language, then its complement, denoted as L', is also a language.
Complement of a Language
The complement of a language L, denoted as L', is the set of all strings that are not in L. In other words, if a string is in L, it is not in L', and vice versa.
Closure under Complement
The closure under complement property states that if a language is accepted by a certain type of automaton, then its complement is also accepted by the same type of automaton.
Closure of Languages Accepted by DPDA
The closure properties of languages accepted by deterministic pushdown automata (DPDA) are as follows:
- Complement: The language accepted by a DPDA is closed under the complement operation. This means that if a language L is accepted by a DPDA, then its complement L' is also accepted by a DPDA.
- Union: The language accepted by a DPDA is not closed under the union operation. This means that if two languages L1 and L2 are accepted by DPDA, their union L1 ∪ L2 may not be accepted by a DPDA.
Explanation
The correct answer is option A, which states that the language accepted by a DPDA is closed under the complement operation. This means that if a language L is accepted by a DPDA, then its complement L' is also accepted by a DPDA. In other words, if a DPDA can recognize a language, it can also recognize its complement.
However, the language accepted by a DPDA is not closed under the union operation. This means that if two languages L1 and L2 are accepted by DPDA, their union L1 ∪ L2 may not be accepted by a DPDA. The union of two languages accepted by a DPDA may require a more powerful computational model, such as a non-deterministic pushdown automaton (NPDA) or a Turing machine, to recognize.
Therefore, the correct answer is option A, as the language accepted by a DPDA is closed under the complement operation but not under the union operation.