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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.

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