• generalization of incrementally verifiable computation from sequential chains to arbitrary DAGs
  • allows multiple independent computations to be combined into a single proof
  • each node in the DAG carries a proof that
    • all predecessor proofs are valid
    • the local computation at this node is correct
  • where incrementally verifiable computation handles a linear chain of steps, PCD handles branching and merging computation paths
  • a node can have multiple parents: it absorbs and combines their proofs via folding into a shared accumulator
  • enables distributed proof generation where different neurons prove different parts of the computation and results are merged
  • constructions
    • built on top of IVC schemes like Nova, HyperNova, Protostar
    • requires a compliance predicate that defines what “valid computation” means at each node
    • the compliance predicate checks predecessor proofs and the local transition function
  • applications in cyber
    • DAG-structured cybergraph verification: the knowledge graph is not a chain but a DAG of cyberlinks, PCD matches this topology naturally
    • parallel validator proving: different validators prove different subgraphs, then merge proofs at shard boundaries
    • cross-shard integrity: when a query spans multiple shards of the cybergraph, PCD combines per-shard proofs into a global certificate
    • multi-agent reasoning: when multiple neurons contribute to a computation (e.g. collective ranking), PCD proves the aggregate is correct without re-executing each contribution
    • authenticated_graphs with fractional cascading: PCD enables composition of proofs across the shard hierarchy described in authenticated_graphs
  • properties
    • succinctness: final proof is small regardless of the DAG size
    • parallelism: independent branches can be proved concurrently
    • composability: any subtree of proofs can be verified independently
    • generality: subsumes incrementally verifiable computation as the special case of a single-path DAG
  • related