A language is recursive if:a.It is recognized by a Turing machine that halts on all inputs.b.It is generated by a context-free grammar.c.It is Turing complete.d.It is closed under concatenation.

A language is considered recursive if it is recognized by a Turing machine that halts on all inputs. This means that for any given input, the Turing machine will eventually stop running, either accepting or rejecting the input.

Here's a step-by-step explanation:

1. A Turing machine is a theoretical machine used in formal language theory and computer science to model computation and algorithmic logic. It reads and writes symbols on an infinite tape according to a set of rules.

2. When we say a language is recognized by a Turing machine, it means that there is a Turing machine which, given a string from the language as input, will eventually halt and accept the string. If the string is not in the language, the Turing machine will reject it.

3. The key point here is that the Turing machine halts on all inputs. This means that no matter what string you give it, the Turing machine will eventually stop running. It won't go into an infinite loop or keep running forever. This is what makes the language recursive.

The other options (b, c, and d) are not necessarily characteristics of a recursive language. A language can be generated by a context-free grammar or be closed under concatenation without being recursive. And Turing completeness is a property of computational