Abstract: A method for accommodating frequent discrete clock synchronization adjustments while maintaining a continuous logical clock time that amortizes the adjustments at a predetermined rate. Two distinct logical clocks are used to decouple clock synchronization procedures from adjustment amortization procedures. One logical clock is discretely synchronized to an external time reference and a second logical clock is adjusted with amortization to provide a continuous monotonically non-decreasing logical clock time.

Abstract: A method and apparatus are disclosed for managing tasks in a network of processors. After a period of time has elapsed, during which the processors of the network have been executing tasks allocated to them, the processors exchange views as to which pending tasks have or have not been completed. The processors reach a consensus as to the overall state of completion of the pending tasks. In a preferred embodiment, the processors exchange views and update their views based on the views received from the other processors. A predetermined condition determines that a consensus has been reached. The predetermined condition is preferably two sets of exchanges in which a processor has received messages from the same set of other processors. Alternatively, the condition is an exchange which does not result in any updates to a processor's view.

Abstract: A method is provided for synchronizing a local time maintained at a node within a network architecture with a reference time. Bursts of synchronization messages containing reference time stamps are transmitted over a network or communication link according to a predetermined protocol. A node to be synchronized receives and time stamps the messages. Thus, times according to a first time scale and a second time scale are obtained, and the protocol defines temporal relationships between certain ones of the times. In accordance with the predetermined protocol, the node determines a difference between a first time according to one of the time scales and a time related to second and third times according to the other time scale. The node then updates its local time based on the difference between the first time and the related time.

Abstract: A method for reliably broadcasting information in a point-to-point network of processors in the presence of component faults provided that the network remains connected using only an exchange of messages. The method possesses the properties (1) that every message broadcast by a fault-free processor is accepted exactly once by all fault-free processors within a bounded time, (2) that every message broadcast is either accepted by all fault-free processors or none of them, and (3) that all messages accepted by fault-free processors are accepted in the same order by all those processors.The method is based on a diffusion technique for broadcasting information and on special message validity tests for tolerating any number of component failures up to network partitioning or successful forgery.

Abstract: A method for synchronizing clocks in a distributed computing system in the presence of faults. The condition to be renewed guarantees that all clocks of correct processors never deviate by more than some maximum amount. This condition is achieved by periodically resynchronizing the clocks so that the correct clocks do not deviate by more than some minimum deviation. In the process of resynchronization, a correct clock is never adjusted by more than a maximum amount during a period and it is never set back.The method requires ascertaining whether a valid time value message has been received within a specified period. A message is valid if it was received within an interval predetermined as a function of the number of signatures from other processors appending the message. If the valid message has not been received within the current period, then the local processor originates and broadcasts to all processors exactly one time value message and appends thereto its unforgeable signature.

Abstract: An originating processor broadcasts a value in a message with its unforgeable signature to all n active processors, including itself. Receiving processors in the network pass such a message on with their own unforgeable signatures to all active processors, including themselves. If the number of signatures and phases is the same at each processor after the first two successive passings, then agreement as to the value with no fault is indicated, otherwise if after two passings, (t+1) signatures have been collected, then these are signed and sent in the third passing, and in any case, each processor continues the steps of repeatedly sending messages when received, and appending its signature until t+2 passings have occurred. At that time, a processor will agree to the value if at least (t+1) signatures append the message, otherwise a default value is adopted, t (n/2) being a reliability measure.

Abstract: A method for synchronizing clocks in a distributed computing system in the presence of faults. The condition to be renewed guarantees that all clocks of correct processors never deviate by more than some maximum amount. This condition is achieved by periodically resynchronizing the clocks so that the correct clocks do not deviate by more than some minimum deviation. In the process of resynchronization, a correct clock is never adjusted by more than a maximum amount during a period and it is never set back.The method requires that there is a previously agreed upon ordered list of all participants. At a specified time in the period, the first processor on the list attempts to synchronize all to its clock. The result of this is either a synchronization of all correct processors and their clocks to be within the desired tolerance or an agreement among all other correct processors that the first node on the list has failed. If the first fails, then the second tries and so on.

Abstract: Weak synchronization and scheduling of each processor among concurrent asynchronous processors is governed by either task execution invoked by an external response indicating its low bid among the well-ordered set of most recently bid signals, task deferred until such indication is received from subsequent bid evaluations, or task aborted as by transfer to another task upon indication that an instantaneous bid was not the minimum.

Abstract: Flow graph related program segments having cyclic paths therethrough are efficiently processed on a SIMD machine by priority ordering the segments, selectively inserting ELSE/JOIN instructions as steps prior to enforcing the ordering when the network of program segments is executed on a SIMD machine.