{"id":"palomar/PALOMAR-2026-09-30-000019","url":"https://github.com/mmislan/palomar-p086-d-stability-conp-hard/tree/4bca0dc5b1d87d12e789cfc817b91db5a84dec37","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-30-000019-v1.json","repo":"https://github.com/mmislan/palomar-p086-d-stability-conp-hard","tags":["math.DS","msc:15A18","msc:68Q17","msc:93D09","dynamical-systems","matrix-stability","computational-complexity"],"score":0,"title":"Deciding D-stability is coNP-hard","trust":"high","domain":"math.DS","source":"palomar","authors":["Michael Mislan"],"reviews":0,"subject":"math.DS","summary":"The computational difficulty of D-stability, raised by Chen, Fan and Yu (1995, doi:10.1016/0167-6911(94)00036-U), is addressed by an explicit integer-matrix reduction from PARTITION. For positive weights of total 2T, the construction produces a matrix of order m + 4 that is D-stable exactly when no subset has weight T. When an equal split exists, some positive diagonal scaling has an eigenvalue with strictly positive real part. A Pell recursion supplies the parameters, with a logarithmic search bound and an explicit bound on every matrix entry. These bounds give polynomial binary output…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-30","reactions":{},"formalized":true,"formalizes":[{"title":"Deciding D-stability is coNP-hard","identifier":"","relationship":"formalizes"}]}