Theorem 3 definition

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

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 the MLE, wˆk, as k 1 + w2ck ckM k gˆe = wkck . √ ζk k − gˆ Σ , (20) | wˆk = arg max f (rk qk, ζk; wk), (15) wk can be factorized as where qk is given by the information reconciliation using a rateless Xxxxxxx-Xxxx code. The pdf f (rk|qk, ζk; wk) in (15) where gˆk is the MMSE estimate of gk in (18). k Proof: From (19), we can find gˆe by conducting a serious of decomposition as follows: x x x x ∫ gˆe = gef (ge|rk, qk, ζk; wk)dge f (rk|qk, ζk; wk) = ∫ ge ∫ f (ge, g |r , q , x ; w )dg dge ∫ = ∫ f (rk|qk, ζk, gk; wk)f (gk|qk, ζk; wk)dgk x x x x x x x x x ∫ ∫ e k

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).

Examples of Theorem 3 in a sentence

• Notice, however, that for this this result to hold Assumption 1 must be satisfied, since this is needed to ensure that the restricted PML estimate,˜θ, from (1) is consistent, as demonstrated in Theorem 3.

• Analyzing the AA protocol, this will imply that, given any process p, its decision values for distinct ids α < β will be at distance at least 1 from each other [19, Theorem 3].

• Assumption 2(b) implies that zt satisfies a functional central limit theorem (Brown, 1971, Theorem 3), since the higher moment assumption implies a conditional Lindeberg condition.

• There is one essential exponentiation, the square-root computation to obtain X¯ in Theorem 3.

• It deals mostly with the protocol aspects; indeed, our cryptographic proof for Theorem 3, conducted with EasyCrypt, concerns less than 200 lines of F#.

• Given that, Theorem 5 is a straightforward consequence of the soundness of the model (Theorem 3).

• By definition, an invalid transaction is one that does not pass one or more of the checks defined in Figure 2 at a shared, for which the shard has erroneously emitted a proposed(T, commit) message.Security Theorem 3.

• Thus there is no path in the chain of possible interleavings of the executions of two conflicting transactions that leads to them both being committed.S-BAC Theorem 3.

• Theorem 3: The following is true for any document set D that has the breadth property.

• Although this will always be true in large samples, see Theorem 3, this could fail with a finite sample size.

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).