Nucleic Acids design targeting integer-valued features: FPT counting and uniform sampling

In this extended abstracts, we describe an approach to account for integer-valued constraints in RNA design. In particular, we describe various FPT/XPT approaches, heavily relying on dynamic programming, for counting and sampling sequences fulfilling a set of declarative constraints. We close this short note with several open questions, drawing connections with graph theory and enumerative combinatorics.