Rational transductions and complexity of counting problems
This work presents an algebraic method based on rational transductions to study the sequential and parallel complexity of counting problems for regular and context-free languages. This approach allows to obtain old and new results on the complexity of ranking and unranking as well as on other problems concerning the number of prefixes, suffixes, subwords and factors of a word which belong to a fixed language. Other results concern a suboptimal compression of finitely ambiguous c.f. languages, the complexity of the value problem for rational and algebraic formal series in noncommuting variables and a characterization of regular and Z-algebraic languages by means of rank functions.
KeywordsFormal Series Regular Language Regulate Representation Counting Problem Constant Space
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