Each circuit family will naturally generate a recursive language by outputting 1 when a string is a member of the family, and 0 otherwise.
12.
Therefore, whenever an ambiguity is possible, the synonym for " recursive language " used is "'Turing-decidable language "', rather than simply " decidable ".
13.
These notions generalize when one considers the circuit complexity of a recursive language : a formal language may contain strings with many different bit lengths.
14.
There are only certain formal metalanguages used for describing recursive languages ( formally called context-free languages ) that have terminals, nonterminals, and metasymbols in their metasyntax.
15.
An example of recursive language that is not context-sensitive is any recursive language whose decision is an EXPSPACE-hard problem, say, the set of pairs of equivalent regular expressions with exponentiation.
16.
Within the Chomsky hierarchy, the regular languages, the context-free languages, and the recursively enumerable languages are all cones, whereas the context-sensitive languages and the recursive languages are only faithful cones.
17.
An example of recursive language that is not context-sensitive is any recursive language whose decision is an EXPSPACE-hard problem, say, the set of pairs of equivalent regular expressions with exponentiation.
18.
However, the language " S " ( " x " ) may not even be a recursive language, since there are uncountably many such " x ", but only countably many recursive languages.
19.
However, the language " S " ( " x " ) may not even be a recursive language, since there are uncountably many such " x ", but only countably many recursive languages.
20.
Let " A " be the set of all regular languages over ? ( or the set of all context-free languages over ?; or the set of all recursive languages over ?; or the set of " all " languages over ? ).
