Sampling Markov Models under Constraints: Complexity Results for Binary Equalities and Grammar Membership

Stephane Rivaud; François Pachet

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arXiv · 1711.10436

Sampling Markov Models under Constraints: Complexity Results for Binary Equalities and Grammar Membership

Stephane Rivaud·François Pachet

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Abstract

We aim at enforcing hard constraints to impose a global structure on sequences generated from Markov models. In this report, we study the complexity of sampling Markov sequences under two classes of constraints: Binary Equalities and Grammar Membership Constraints. First, we give a sketch of proof of #P-completeness for binary equalities and identify three sub-cases where sampling is polynomial. We then give a proof of #P-completeness for grammar membership, and identify two cases where sampling is tractable. The first polynomial sub-case where sampling is tractable is when the grammar is proven to be unambiguous. Our main contribution is to identify a new, broader class of grammars for which sampling is tractable. We provide algorithm along with time and space complexity for all the polynomial cases we have identified.

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BibTeX RIS

Stephane Rivaud, François Pachet. 2017-11-28. Sampling Markov Models under Constraints: Complexity Results for Binary Equalities and Grammar Membership. https://arxiv.org/abs/1711.10436

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