Algorithm. We now describe an algorithm that solves Byzantine agree- ment in the basic partially synchronous model when ℓ > n+3t . Our algorithm is based on the algorithm given by Xxxxx, Xxxxx and Xxxxxxxxxx [9] for the classical case where n = ℓ, with several novel features. Generalizing the algo- rithm is not straightforward. Some of the difficulty stems from the following scenario. Suppose two correct processes share an identifier and follow the traditional algorithm of [9]. They could send very different messages (for example, if they have different input values), but recipients of those messages would have no way of telling apart the messages of the two correct senders, so it could appear to the recipients as if a single Byzantine process was sending out contradictory information. Thus, the algorithm has to guard against in- consistent information coming from correct homonym pro- cesses as well as malicious messages sent by the Byzantine processes.
Algorithm. Next, we present an algorithm that solves Byzantine agree- ment assuming ℓ > 3t. Our agreement algorithm is generic: given any synchronous Byzantine agreement algorithm for ℓ processes with unique identifiers (such algorithms exist when ℓ = n > 3t, e.g., [13]), we transform it into an algorithm for n processes and ℓ identifiers, where n ≥ ℓ. Without loss of generality, we assume that the algorithm to be transformed uses broadcasts: a process sends the same message to all other processes. (If a process wishes to send a message only to specific recipients, it could include the recipient’s identi- fier in the broadcasted message.) In our transformation, we divide processes into groups ac- cording to their identifiers. Each group simulates a single process. If all processes within a group are correct, then they can reach agreement and cooperatively simulate a sin- gle process. If any process in the group is Byzantine, we allow the simulated process of that group to behave in a Byzantine manner. The correctness of our simulation re- lies on the fact that more than two-thirds of the simulated processes will be correct (since ℓ > 3t), which is enough to achieve agreement.
Algorithm. We now describe the basic step of the reconciliation mechanism, i.e., the reconcili- ation between two sites on a given object. Section 8 describes when to invoke the reconciliation mechanism, and the options that exist in its use. The basic step is as follows.
Algorithm. Prior to GEMS commencing --------- discussions with the Institutional Review Board ("IRB"), R2 shall confirm in writing to GEMS that the R2 Product algorithm can process the PMA (pre-market approval) cases which are done in feasibility format and that R2 can use them for the PMA submission. In the event that the FDA does not accept these cases for R2's FDA submission, then GEMS and R2 shall negotiate in good faith to determine how to acquire additional cases as outlined in Section 2.8.3.
Algorithm. The shared memory Under x-obstruction-freedom, up to x processes may concurrently progress without preventing termination. As a consequence, in comparison to obstruction-freedom, solving k-set agreement in this setting requires to deal with more contention scenarios. To cope with these additional interleavings of processes, we increase the number of entries in REG . More precisely, REG now contains m = (n − k + x) entries. Ordering the quadruplets In the base algorithm, the four fields of some quadruplet X are the round number X.rd, the level X.ℓvℓ, the conflict flag X.xxℓ, and the value X.val. Coping with x-concurrency requires to replace the last field, which was initially a singleton, with a set of values. Hereafter, this new field is denoted X.valset. In line with the definitions of Section 4.1, let “>” denote the lexicographical order over the set of quadruplets, where the relation ⊐ is generalized as follows to take into account the fact that the last field of a quadruplet is now a non-empty set of values: X ⊐ Y d=ef (X > Y ) ∧ [(X.rd > Y.rd) ∨ (X.xx ℓ) ∨ (X.valset ⊇ Y.valset)]. In comparison to the definition appearing in Section 4, the sole new case where the ordering X ⊐ Y holds is (X > Y ) ∧ (X.valset ⊇ Y.valset). This case captures the fact that, as long as at most x input values are competing at some round, there is no conflict. If such a situation arises, we simply construct a quadruplet that aggregates the different input values. function sup(T ) is % T is a set of quadruplets whose last field is now a set of values % (S1) (S2) (S3) (S4) (S5) (S6) let (r, ℓeveℓ, conf ℓict, valset ) be max(T ); let tuples(T ) be {X | X ∈ T ∧ X.rnd = r}; let values(T ) be {v | X ∈ T ∧ v ∈ X.valset }; let conf ℓict (T ) be conflict ∨ |tuples(T )| > x ∨ |values(T )| > x; % lexicographical order % l et valset be the (at most) x greatest values in values(T ); return (r, ℓeveℓ, conf ℓict (T ), valset ) . Figure 4: Function sup() suited to x-obstruction-freedom Modifications to the sup() function Figure 4 describes the new definition of function sup(). Compared with the original algorithm in Figure 1, it introduces a few modifications (underlined and in blue). Those are detailed below. • Line S1. As pointed out previously, the last field of a quadruplet is now a set of values. The lexicographical ordering over such sets is as follows: sets are ordered first according to their size, and second using some arbitrary order over their elements. By abuse of notation, this ...
Algorithm. This Agreement is for the use of one algorithm in connection with transaction verification for one or more blockchain protocols. At the commencement of the Term of the Agreement, the Customer-selected algorithm may be employed for certain digital assets extraction. As described in Section 3 below, the Customer acknowledges the risks associated with blockchain technologies and acknowledges that variations may occur with the protocols used to perform blockchain transaction verifications (“output”) for cryptocurrencies using the algorithm selected by the Customer.
Algorithm. We present an oblivious algorithm for solving the point convergence problem. (As we show later, the algorithm solves the point formation problem if the robots are synchronous.) Intuitively, the algorithm solves the problem by achieving the fol- lowing two subgoals at every time instant t:
(1) the robots in the same connected component of Gt \get closer" in some sense at t+1, and (2) robots that are mutually visible at t remain mutually visible at t + 1. First of all, at every time instant t, if ri does not see any robot other than itself then ri does not move at t. Otherwise to achieve the rst subgoal, we move ri toward the center ci(t) of the smallest enclosing circle Ci(t) of the positions of all the robots that ri can see, over some distance M OV E to be speci ed below. See Figure 7. If ri moves at t as mentioned above, then we achieve the second subgoal as x x(t) x x Figure 8: Robots ri and rj remain mutually visible. follows. Let rj, i 6= j, be one of the robots that are visible from ri at t. Let mj be the midpoint of ri(t) and rj(t). As is shown in Figure 8, if the next positions of ri and rj are both inside the disc Dj with center mj and radius V =2, then ri and rj can still see each other at t + 1. Formally, given the direction of the move (towards ci(t), as explained above), ri computes the maximum distance `j that it can move in that direction with- out leaving Dj, as follows. If dist(ri(t); rj(t)) = 0, then clearly `j = V =2. Oth- erwise, let dj = dist(ri(t); rj(t)) be the distance between ri and rj at t, and j = 6 ci(t)ri(t)rj(t) the direction of the move of ri with respect to the ray from ri to rj, where 0 j . Then `j = (dj=2) cos j + q(V =2)2 ((dj=2) sin j)2: Robot ri computes this `j for each rj 2 Si(t), and then nds rj 2Si(t) frig f`jg GOAL = dist(ri(t); ci(t)); which is the distance from ri to ci(t) at t. Finally, ri moves over distance M OV E = minfGOAL; XXX IT g towards ci(t). By the de nition of LIM IT , ri remains inside the disc Dj for every rj 2 S after the move. Since all robots compute their next positions using the same algorithm, any pair of robots that are mutually visible at t remain mutually visible at t + 1. That is: Lemma 5 For any two robots ri, rj and any time instant t 0, (ri; rj) 2 Et ! (ri; rj) 2 Et+1. 2
Algorithm. Diagnoeasy algorithm for the listing is an automated system that is able to list profiles of the Diagnostic Center s and information regarding the practices in the website and app. These listings do not translate to any fixed objectives, rankings, or endorsements by Diagnoeasy. Diagnoeasy will not be liable for any change in the search results, which may take place from time to time. The listing of the Diagnostic Center s will be based on the automated computation of various factors and criteria including inputs from users including other user’s comments and feedback. Such factors may change from time to time. Diagnoeasy in no event will be held responsible for the accuracy or relevancy or repeatability of the listing or listing orders of the Diagnostic Center s on the website or app.
Algorithm. Many AA protocols in the literature, whether they work with scalars [1, 4, 13, 20], multiple dimensions [26, 32], or even graphs or lattices [29], follow a similar structure: they operate in multiple iterations. In each iteration, the parties first distribute their current values. Then, the parties discard the outliers out of the values received, and compute a new value based on the values remaining. To achieve AA, each iteration should satisfy a few properties. Firstly, the values obtained by the honest parties should be in the convex hull of the values they started the iteration with, to ensure Validity. Secondly, the values obtained by the honest parties should get closer, to ensure that 𝜀-Agreement is eventually achieved. In our model, or even in the purely synchronous model, it is also essential to maintain the honest parties synchronized, similarly to [20]. These properties roughly ensure that, after a sufficient number of iterations, 𝐷-AA is achieved. For our AA protocol, we implement the steps taken in a single iteration in a subroutine called ΠAA-it. It is also important to define the sufficient number of iterations. While some known AA protocols [20, 29] predefine this number (by assuming that some bounds on the input space are known), others allow the parties to estimate the range of honest inputs on their own [1, 26]. Our algorithm will extend this latter approach to the hybrid network model. Then, our protocol proceeds as follows: the parties first run a subroutine Πinit, which enables each honest party to obtain a value 𝑣0 (within the convex hull of the honest inputs) and an estimation 𝑇 (computed accordingly to the convergence guarantees of ΠAA-it). Πinit ensures that 𝑇 iterations of ΠAA-it, starting from the values 𝑣0 it provides instead of the honest parties’ inputs, are enough to achieve 𝐷-AA. This is the case even if 𝑇 is the smallest honest estimation. − Hence, honest parties join the first iteration using 𝑣0 as their initial values. In each iteration it, they run the subroutine ΠAA-it with input 𝑣it 1, defined below, and obtain a new value 𝑣it. When a party 𝑃 reaches iteration it = 𝑇 , matching its own + estimation for when it is safe to output a value, it sends a halt message for iteration it. 𝑃 outputs when it receives 𝑡𝑠 1 halting messages for previous iterations, hence at least one honest halting 10: Output 𝑣itℎ and break +
Algorithm. GRAPHICAL AUTHENTICATION A graphical password is an authentication system that works by having an user select from images in a specific order presented in a graphical user interface (GUI).