IndisputableMonolith.Complexity.ComputationBridge
ComputationBridge introduces dual complexity parameters Tc and Tr to characterize recognition-complete problems. Researchers resolving P versus NP via Recognition Science cite it to link RS constraints with vertex cover instances. The module assembles imported definitions from VertexCover, RSVC, and Recognition without internal theorems.
claimRecognition-complete complexity is characterized by the dual parameters $T_c$ and $T_r$.
background
The module sits in the Complexity domain. It imports VertexCover, which supplies complexity pairs as functions of input size, and RSVC, which maps RS constraint instances to edges to be covered. LedgerUnits provides the subgroup of integers generated by delta, specialized to delta equals 1 for an order isomorphism, while Core.Recognition supplies the underlying recognition structures.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the dual parameters Tc and Tr that feed CellularAutomata. That module constructs local gadgets for Boolean operations and shows SAT evaluation by cellular automata runs in O(n to the 1/3 log n) time, advancing the P versus NP resolution.
scope and limits
- Does not specify explicit functional forms for Tc and Tr.
- Does not contain proofs of recognition completeness.
- Does not implement or simulate cellular automata gadgets.
- Does not state the full P versus NP theorem.
used by (1)
depends on (5)
declarations in this module (14)
-
structure
RecognitionComplete -
structure
TuringModel -
structure
LedgerComputation -
structure
SATLedger -
structure
RecognitionScenario -
def
demoRecognitionScenario -
theorem
Turing_incomplete -
theorem
P_vs_NP_resolved -
structure
ClayBridge -
theorem
clay_bridge_theorem -
theorem
ledger_forces_separation -
structure
Validation -
structure
CompleteModel -
theorem
main_resolution