  This paper introduces a new consensus protocol, so-called \emph{\stair}, for
fast consensus in DAG-based trustless system. In \stair, we propose a new
approach to creating local block DAG, namely \emph{x-DAG} (cross-DAG), on each
node. \emph{\stair} protocol is based on our Proof-of-Stake StakeDag framework
\cite{stakedag} that distinguishes participants into users and validators by
their stake. Both users and validators can create and validate event blocks.
Unlike StakeDag's DAG, x-DAG ensures that each new block has to have parent
blocks from both Users and Validators to achieve more safety and liveness. Our
protocol leverages a pool of validators to expose more validating power to new
blocks for faster consensus in a leaderless asynchronous system. Further, our
framework allows participants to join as observers / monitors, who can retrieve
DAG for post-validation, but do not participate in onchain validation.
