As we know, formal language can be regarded as a set of strings of alphabet, and real number can be regarded as sequence generated by set of integers, for example, denominators of the simple continued fraction may form a set.

Algorithms analyze language and algorithms decide or output set of integers generating reals. Now, are the any transformation correspondence between language and real number, which keep the computational complexity in the same class? As we know, Godel encoding may be such a kind of transformation. Any reference?

Also, we hope the transformation is inverse.

As we know, formal language can be regarded as a set of strings of alphabet, and real number can be regarded as sequence generated by set of integers, for example, denominators of the simple continued fraction may form a set.

Algorithms analyze language and algorithms decide or output set of integers generating reals. Now, are there any transformation or correspondence between language and real number, which keep the computational complexity in same class? As we know, Godel encoding may be such a kind of transformation. Any reference?

Also, we hope the transformation is bijective.