Random Generation and Approximate Counting of Ambiguously Described Combinatorial Structures

Abstract

This paper concerns the uniform random generation and the approximate counting of combinatorial structures admitting an ambiguous description. We propose a general framework to study the complexity of these problems and present some applications to specific classes of languages. In particular, we give a uniform random generation algorithm for finitely ambiguous context-free languages of the same time complexity of the best known algorithm for the unambiguous case. Other applications include a polynomial time uniform random generator and approximation scheme for the census function of (i) languages recognized in polynomial time by one-way nondeterministic auxiliary pushdown automata of polynomial ambiguity and (ii) polynomially ambiguous rational trace languages.Keywordsuniform random generationapproximate countingcontext-free languagesauxiliary pushdown automatarational trace languagesinherent ambiguity