## Ranking and formal power series.(English)Zbl 0721.68023

The ranking problem for a language $$L\subseteq A^*$$ is the following: given w in L, compute the integer n such that w is the n-th element of L for the lexicographic order (u$$\leq v$$ if either $$| u| <| v|$$ or $$| u| =| v|$$ and u precedes v alphabetically). The value problem for noncommutative formal series $$S\epsilon {\mathbb{N}}\ll X\gg$$ is the following: given w in $$X^*$$, compute the coefficient of w in S.
The authors show that the ranking problem for an unambiguous context-free language is $$NC^ 1$$-reducible to the value problem for an algebraic formal series. An application to regular languages is given.

### MSC:

 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.) 68Q45 Formal languages and automata

### Keywords:

parallel complexity; ranking
Full Text:

### References:

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