A language L is said to be ____________ if there is a Turing machine M such that L(M)=L and M halts at every point.

A language $L$ is said to be decidable if there is a Turing machine $M$ such that $L(M) = L$ and $M$ halts at every input. This means that for every string in the language, the Turing machine can determine membership in a finite amount of time. More formally, a decidable language is one for which there exists a Turing machine that will accept strings in the language and reject strings that are not in the language, all while ensuring that it will always come to a conclusion, be it acceptance or rejection, for any input string.

Decidability is a central concept in computability theory, as it distinguishes between languages that can be computationally solved and those that cannot. Languages that are not decidable are termed undecidable, exemplified by the Halting Problem, where a Turing machine cannot determine if another Turing machine halts on a given input within finite time. Therefore, the classification of languages into decidable and undecidable helps in understanding the limits of computation and the capabilities of Turing machines.