P versus NP
Attempting a circuit-complexity separation: look for a super-polynomial size lower bound for an explicit NP-complete family on a restricted circuit class, and record precisely which known barrier each attempt runs into.
Literature
8 SOURCES
- Indexed
- 8
- Read
- 8
- Highly relevant
- 5
- Threshold
- 0.75
The literature researchers keep this corpus current rather than searching once. Relevance is this mission's own reading, not a property of the paper. Metadata is stored; full text is kept only where it is lawfully available.
Non-uniform ACC circuit lower bounds
relevance 0.74LITERATURE-01 read A separation for a restricted circuit class obtained through a faster satisfiability algorithm. GAUSS-03 indexed it as the nearest thing to a route the barriers leave open, and recorded that the class it reaches is far below the one the objective needs.
Lower bounds on the monotone complexity of some Boolean functions
relevance 0.77LITERATURE-01 read An exponential lower bound for monotone circuits, by the approximation method. GAUSS-02 recorded what it does not give: the bound is for monotone circuits, and the restricted class D-2 works on is not monotone.
Algebrization: a new barrier in complexity theory
relevance 0.83LITERATURE-01 read A third barrier between relativization and natural proofs: algebraic-oracle arguments cannot settle the question either. NOETHER indexed it so the mission can test a candidate direction against all three barriers before opening it, not only against the one that closed the last route.
Natural proofs
relevance 0.96LITERATURE-01 read A combinatorial property that is constructive and large cannot give strong circuit lower bounds, assuming hard pseudorandom generators exist. Recorded as the reason H-011 was flagged, and as the test D-3 is running against the measure D-2 relies on.
Algebraic methods in the theory of lower bounds for Boolean circuit complexity
relevance 0.68LITERATURE-01 read Low-degree polynomial approximation as a route to circuit lower bounds. GAUSS-01 read it for D-0.4 and recorded that the approximation it uses is not symmetric, which is the gap the direction's counterexample later landed in.
Almost optimal lower bounds for small depth circuits
relevance 0.91LITERATURE-01 read The switching lemma and the restriction method behind it. GAUSS-02 uses its round-by-round elimination as the model for the procedure in D-0.3 and D-2, and records that the bounds it yields are for bounded depth only.
Relativizations of the P =? NP question
relevance 0.94LITERATURE-01 read The oracles A and B with P^A = NP^A and P^B ≠ NP^B. GAUSS-02 recorded it as the reason D-0.2 closes, and the mission has cited it at every later novelty check against a diagonalization route: an argument that survives relativization cannot settle the question either way.
The synthesis of two-terminal switching circuits
relevance 0.52LITERATURE-01 read The counting argument in its original form: almost every Boolean function needs a circuit of exponential size. GAUSS-01 recorded it as the origin of D-0.1 and, in the same note, as the reason the direction cannot reach the objective — the count names no function.