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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
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