  Consensus stands as a fundamental building block for constructing reliable
and fault-tolerant distributed services. The increasing demand for
high-performance and scalable blockchain protocols has brought attention to
solving consensus in scenarios where each participant joins the system knowing
only a subset of participants. In such scenarios, the participants' initial
knowledge about the existence of other participants can collectively be
represented by a directed graph known as knowledge connectivity graph. The
Byzantine Fault Tolerant Consensus with Unknown Participants (BFT-CUP) problem
aims to solve consensus in those scenarios by identifying the necessary and
sufficient conditions that the knowledge connectivity graphs must satisfy when
a fault threshold is provided to all participants. This work extends BFT-CUP by
eliminating the requirement to provide the fault threshold to the participants.
We indeed address the problem of solving BFT consensus in settings where each
participant initially knows a subset of participants, and although a fault
threshold exists, no participant is provided with this information -- referred
to as BFT Consensus with Unknown Participants and Fault Threshold (BFT-CUPFT).
With this aim, we first demonstrate that the conditions for knowledge
connectivity graphs identified by BFT-CUP are insufficient to solve BFT-CUPFT.
Accordingly, we introduce a new type of knowledge connectivity graphs by
determining the necessary and sufficient conditions they must satisfy to solve
BFT-CUPFT. Furthermore, we design a protocol for solving BFT-CUPFT.
