Are regular languages recursive?

1 Answer. Regular languages are accepted by finite automata, which have no usable memory. … A recursive language is one that can be decided by a Turing machine, which has a (potentially) infinite tape for memory. Regular languages are recursive because you can make a TM equivalent to a FA by not using the tape./span>

Note: A language is Recursively enumerable (RE) but not recursive (REC) then it complement is non-RE. option E is false./span>

A recursive language is a formal language for which there exists a Turing machine that, when presented with any finite input string, halts and accepts if the string is in the language, and halts and rejects otherwise.

Recursively enumerable languages are closed under complement. Proof. Same as previous machine. This fails because M only needs to halt if w in L(M) – doesn’t have to say “no”.

Union Both decidable and Turing recognizable languages are closed under union.

Explanation: Every recursive language is recursively ennumerable but there exists recursively ennumerable languages that are not recursive. If L is accepted by a Non deterministic TM T, and every possible sequence of moves of T causes it to halt, then L is recursive.

P is closed under complement. For any P-language L, let M be the TM that decides it in polynomial time. We construct a TM M’ that decides the complement of L in polynomial time: M’= “On input : … Since M runs in polynomial time, M’ also runs in polynomial time.

NP is closed under union, intersection, and concatenation; but is not known to be closed under complement.

A class is said to be closed under complement if the complement of any problem in the class is still in the class. … Any class which is closed under complement is equal to its complement class.

Decidable languages are closed under concatenation and Kleene Closure. Proof. Given TMs M1 and M2 that decide languages L1 and L2. A TM to decide L1L2: On input x, for each of the |x| + 1 ways to divide x as yz: run M1 on y and M2 on z, and accept if both accept.

A language is called Decidable or Recursive if there is a Turing machine which accepts and halts on every input string w. Every decidable language is Turing-Acceptable. A decision problem P is decidable if the language L of all yes instances to P is decidable.

In grammar, a complement is a word, phrase, or clause that is necessary to complete the meaning of a given expression. Complements are often also arguments (expressions that help complete the meaning of a predicate).

Up vote 5. An example of a language which is not recursively enumerable is the language L of all descriptions of Turing machines which don’t halt on the empty input./span>