This paper introduces a new reconfiguration problem of matchings in a triangular grid graph. In this problem, we are given a nearly perfect matching in which each matching edge is labeled, and aim to transform it to a target matching by sliding edges one by one. This problem is motivated to investigate the solvability of a sliding-block puzzle called "Gourds" on a hexagonal grid board, introduced by Hamersma et al. [ISAAC 2020]. The main contribution of this paper is to prove that, if a triangular grid graph is factor-critical and has a vertex of degree 6, then any two matchings can be reconfigured to each other. Moreover, for a triangular grid graph (which may not have a degree-6 vertex), we present another sufficient condition using the local connectivity. Both of our results provide broad sufficient conditions for the solvability of the Gourds puzzle on a hexagonal grid board with holes, where Hamersma et al. left it as an open question.

A proof-of-concept non-binary cyclic ADC with proposed correlated level shifting (CLS) technique is designed and fabricated in 90nm CMOS technology. By applying the odd/even structure to a multiplying digital-to-analog converter (MDAC), the amplifier with CLS can be used for a cyclic ADC, so that the allowable dynamic range of the proposed cyclic ADC almost is doubled comparing to the conventional cyclic ADC. As a result, the SNDR of ADC can be improved with smaller power penalty. Measurement results of the prototype confirm the effectiveness of the proposed CLS technique for cyclic ADC.