Markov processes are increasingly used to generate finite-length sequences that imitate a given style. However, Markov processes are notoriously difficult to control. Recently, Markov constraints have been introduced to give users some control on generated sequences. Markov constraints reformulate finite-length Markov sequence generation in the framework of constraint satisfaction (CSP). However, in practice, this approach is limited to local constraints and its performance is low for global constraints, such as cardinality or arithmetic constraints. This limitation prevents generated sequences to follow structural properties which are independent of the style, but inherent to the domain, such as meter. In this article, we introduce meter, a constraint that ensures a sequence is 1) Markovian with regards to a given corpus and 2) follows metrical rules expressed as cumulative cost functions. Additionally, meter can simultaneously enforce cardinality constraints. We propose a domain consistency algorithm whose complexity is pseudo-polynomial. This result is obtained thanks to a theorem on the growth of sumsets by Khovanskii. We illustrate our constraint on meter-constrained music generation problems that were so far not solvable by any other technique.

Many systems use Markov models to generate finite-length sequences that imitate a given style. These systems often need to enforce specific control constraints on the sequences to generate. Unfortunately, control constraints are not compatible with Markov models, as they induce long-range dependencies that violate the Markov hypothesis of limited memory. Attempts to solve this issue using heuristic search do not give any guarantee on the nature and probability of the sequences generated. We propose a novel and efficient approach to controlled Markov generation for a specific class of control constraints that 1) guarantees that generated sequences satisfy control constraints and 2) follow the statistical distribution of the initial Markov model. Revisiting Markov generation in the framework of constraint satisfaction, we show how constraints can be compiled into a non-homogeneous Markov model, using arc-consistency techniques and renormalization. We illustrate the approach on a melody generation problem and sketch some realtime applications in which control constraints are given by gesture controllers.