Theorem 3 definition

Theorem 3. AdvPA' (t, qex, qs) ≤ (qs + 2qex) ∗ SuccDDH 2k q +qexqs (t′)+ |P| ∗ SuccΣ(t′)+ s

Split View

AI-Powered Contracts

Draft, Review & Redline at the Speed of AI

Get StartedSchedule a Demo

Theorem 3. For MSP k, the optimal BS switching on/off strategies are as follows: turn off if V (a)(on, on) < V (a)(off, on) + Ek and its QoS commitment is honored (case Ak); turn on otherwise (i.e., either turning off leading to QoS commitment violation (case Bk) or V (a)(on, on) > V (a)(off, on) + Ek (case Ck)). The proof is straightforward by recalling the utility defini- tion above. The NEs for the BS switching on/off game are then stated 1, and reward rate of MSP 2 vs. β1 and β2, respectively (lower bounds in S2).

Theorem 3. For given rk, qk, and ζk, the MMSE estimator for ge is given by normalized received signal vector at Bob in (6), we can derive 1 + w2ck ckM the MLE, wˆk, as gˆe = wkck √ζk − gˆ , (20) wˆk = arg max f (rk qk, ζk; wk), (15) wh where qk is given by the information reconciliation using a rateless ▇▇▇▇▇▇▇-▇▇▇▇ code. The pdf f (rk|qk, ζk; wk) in (15) can be factorized as where gˆk is the MMSE estimate of gk in (18). Proof: From (19), we can find gˆe by conducting a serious of decomposition as follows: gef (ge|rk, qk, ζk; wk)dge ∫ gˆe = f (rk|qk, ζk; wk) = ∫ ge ∫ f (ge, g |r , q , ▇ ; w )dg dge ∫ = ∫ f (rk|qk, ζk, gk; wk)f (gk|qk, ζk; wk)dgk

Examples of Theorem 3 in a sentence

• Note that Theorem 3 implies the Liveness property of our Lattice Agreement specification.

• It follows from Theorem 3 that the 3ROM algorithm always guarantees agreement at the good nodes in three rounds and regardless of a particular value of F.

• By reflecting this violation below κ, we contradict our assumption that there was a level-by- level agreement there, and the proof of Theorem 3 is complete.

• Extraction and robustness (which here means that neither i nor M can be modified without detection) are proved in a manner very similar to the proof of Theorem 3.

• Before concluding this section, we would like to call attention to the fact that our proof of Theorem 3 does not fully use the hypothesis that κ is an indestructible supercompact cardinal.

• Bisimulations on different systems ⇒ The validity of the implication (3) (1) of Theorem 3 is shown in ▇▇▇▇ and Schro¨der (2000), based on the standard notion of bisimulation on different systems: given F- coalgebras (X, αX) and (Y, αY ) a relation R ⊆ X × Y is a bisimulation if there exists a transition structure γ : R → FR such that the following diagram commutes: π1 π2 R z,Y .,,r ,.

• Specifically, Theorem 3 establishes that if one has a level-by-level agreement and a supercompact cardinal κ that is indestructible by iterated ▇▇▇▇▇ forcing, then no larger cardinal λ is 2λ-supercompact.

• In the following, we first show that the proposed scheme can provide perfect forward secrecy by using Theorem 3.

• We proceed to show that in Set, if bisimulations on single systems are closed under composition, then bisimulations on different systems are closed under composition as well; this proves that the implication from (3) to (1) of Theorem 3 holds in our setting as well.

• Theorem 3 (Instantiation of our NIZK and commitment schemes [17]).

More Definitions of Theorem 3

Theorem 3. The new upper bound represents a strict improvement over the previously best known upper bound for the case of u = m = 2: there exists an example for which the new upper bound is strictly smaller than supp(x1) infZ→Z→X1X2 I(X1; X2|Z) which in turn is always less than or equal to infZ→Z→X1X2 supp(x1) I(X1; X2|Z).