Algorithm Sample Clauses

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 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 ▇▇▇▇▇, ▇▇▇▇▇ and ▇▇▇▇▇▇▇▇▇▇ [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. 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 ▇.▇▇ℓ, 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) ∨ (▇.▇▇ 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. The agents in this case study are based on the Toshiba DOTS, developed at the Bristol Robotics Laboratory [15] (although it should be noted that the DOTS have more hardware and capabilities than the agents simulated in these experiments). Each agent has the following (simulated) hardware: holonomic wheel configuration; lifting mechanism for items; camera and IR sensor to detect items and obstacles; sensor to communicate with other agents. Using this onboard equipment, each agent can perform the following behaviours every time step: Random Walk; Collision avoidance; Item detection, pick up and put down; Periodic reshuffling of items; Delivery area detection, timer broadcast and item delivery; Swarm Diffusion-Taxis algorithm [16]. The random walk behaviour is updated every 1 second (once every 50 time steps). The agents move forward at a constant speed of 1 m/s for 1 second and then change to a new random direction of movement, adding −0.5c < αrandom < 0.5c to the current direction of travel, α. This is modelled as an instantaneous change in direction. The agents follow this random walk unless something comes into their sensory range. If they come within 0.35 m (centre- centre) of an obstacle then their collision avoidance behaviour is triggered. If the obstacle is a wall then the agent adds a quarter turn to their heading direction (α = α+π/2) until they are moving away from the wall. If the obstacle is another agent or an item (which they want to avoid because they have an item currently) then the agent will move in the opposite direction from that obstacle. If there are multiple obstacles to avoid then the distances and directions to each obstacle sum to a vector, which the agent moves along to avoid them. Item detection, pick up and put down: When an agent that is not currently carrying an item comes into sensory range of an item (0.75 m from agent centre) then the agent will pick up the item. The items are on table-like carriers, which raise them off the ground on stilts. The agents can navigate underneath an item they have found and lift it up from beneath to carry it around. This is based on how items are stored and collected in the Toshiba test-bed, which simulates warehouse scenarios [15]. The items are periodically reshuffled by the agents which will carry items around and put them down again somewhere else if they are not the requested item. They generate a random number between 0 and 100 every time step and if it is below 2 then they drop their i...

Algorithm. The time of arrival information shall be determined using a predictive algorithm that utilizes the current AVL information for the approaching buses to a bus stop. AIM shall calculate the arrival times for all buses up to the next 60 minutes and display up to the next five buses that will arrive at each stop. If more than five buses, the user can scroll to see the additional bus arrivals. The time of arrival information shall be updated at least every thirty seconds and made available to the systems using such information within one second after the AIM server receives a location update. AIM shall also calculate time of departure information which shall be used for announcements for the first stop for each bus route trip. The accuracy of the predictive algorithm shall be such that the predicted error shall be less than 75 seconds when a bus is five minutes or less from a stop; and less than two minutes when a bus is between six and 10 minutes from a stop. The AIM predictive algorithm shall be a learning algorithm that is based on historical data for the stop location, route, and the time of day, day of week, and week of year.

Algorithm. Consider a cluster-based infrastructure-less network with cluster-head ‘CH’ and several cluster members. Consider two cluster members CMA and CHB want to authenticate each other. The public information about the cluster is, {PN, IDCH, IDCMA, IDCMB, TKprh (PN)} , Hash function, symmetric encipherment. Step1: Cluster member CMA selects the Private key Kprcma and calculate the value of TKpr𝔀ma (PN) and KCH−CMA = TKpr𝔀ma TKprh (PN) with the help of public information. Then CMA constructs the message mCMA as follows mCMA = {IDCMA, IDCMB, IDCH, TKpr𝔀ma (PN), CTCMA} Where, CTCMA = E (KCH−CMA, {IDCMA||IDCMB||IDCH||HCMA}) HCMA = {IDCMA||IDCMB||IDCH||TKpr𝔀ma (PN)} Cluster member CMA sends the mCMA to ‘CH, and this message indicates that it wants to authenticate with Cluster member CMB

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. The algorithm consists of two phases. During the first phase, the checkpoint initiator identifies all processes with which it has communicated since the last checkpoint and sends them a request. • Upon receiving the request, each process in turn identifies all processes it has communicated with since the last checkpoint and sends them a request, and so on, until no more processes can be identified. • During the second phase, all processes identified in the first phase take a checkpoint. The result is a consistent checkpoint that involves only the participating processes. • In this protocol, after a process takes a checkpoint, it cannot send any message until the second phase terminates successfully, although receiving a message after the checkpoint has been taken is allowable.