eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-08-31
23:1
23:18
10.4230/LIPIcs.ESA.2021.23
article
Covert Computation in Staged Self-Assembly: Verification Is PSPACE-Complete
Caballero, David
1
Gomez, Timothy
1
Schweller, Robert
1
Wylie, Tim
1
Department of Computer Science, University of Texas Rio Grande Valley, Edinburg, TX, USA
Staged self-assembly has proven to be a powerful abstract model of self-assembly by modeling laboratory techniques where several nanoscale systems are allowed to assemble separately and then be mixed at a later stage. A fundamental problem in self-assembly is Unique Assembly Verification (UAV), which asks whether a single final assembly is uniquely constructed. This has previously been shown to be Π^{p}₂-hard in staged self-assembly with a constant number of stages, but a more precise complexity classification was left open related to the polynomial hierarchy.
Covert Computation was recently introduced as a way to compute a function while hiding the input to that function for self-assembly systems. These Tile Assembly Computers (TACs), in a growth only negative aTAM system, can compute arbitrary circuits, which proves UAV is coNP-hard in that model. Here, we show that the staged assembly model is capable of covert computation using only 3 stages. We then utilize this construction to show UAV with only 3 stages is Π^{p}₂-hard. We then extend this technique to open problems and prove that general staged UAV is PSPACE-complete. Measuring the complexity of n stage UAV, we show Π^{p}_{n - 1}-hardness. We finish by showing a Π^{p}_{n + 1} algorithm to solve n stage UAV leaving only a constant gap between membership and hardness.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol204-esa2021/LIPIcs.ESA.2021.23/LIPIcs.ESA.2021.23.pdf
self-assembly
covert computation
staged self-assembly
assembly verification