Number Of Execution Steps Research Articles

Mechanisation of the AKS Algorithm

The AKS algorithm (by Agrawal, Kayal and Saxena) is a significant theoretical result, establishing “PRIMES in P” by a brilliant application of ideas from finite fields. This paper describes an implementation of the AKS algorithm in our theorem prover HOL4, together with a proof of its correctness and its computational complexity. The complexity analysis is based on a conservative computation model using a writer monad. The method is elementary, but enough to show that our implementation of the AKS algorithm takes a number of execution steps bounded by a polynomial function of the input size. This establishes formally that the AKS algorithm indeed shows “PRIMES is in P”.

Resource management for raft consensus protocol

Protocols which solve agreement problems are essential building blocks for fault-tolerant distributed applications. Especially, many consensus protocols have been proposed in recent decades. Paxos is the most famous consensus protocol, but it is difficult to understand and even more to implement. The recently proposed raft consensus protocol is a leader based consensus protocol. It is a simple enough to understand itself. Given the popularity of cloud-based elastic environments, it should consider adapting such environments. This paper proposes a resource management mechanism for raft protocol. It realises a dynamic raft cluster by introducing the flexible resource management and the notion of suspended nodes. In this mechanism, a leader node arouses suspended nodes when some nodes failed, or nodes come up against a heavy load. It can realise an appropriate configuration on the number of nodes in a service. As a result, it can reduce energy consumption during execution. Then, we show the performance evaluation of the proposed protocol regarding the number of messages sent by nodes and the number of execution steps for consensus executions. We also show the message-efficiency and the cost for the resource management mechanism by comparing the proposed protocol with raft protocol.

The Static Parallelization of Loops and Recursions

We demonstrate approaches to the static parallelization of loops and recursions on the example of the polynomial product. Phrased as a loop nest, the polynomial product can be parallelized automatically by applying a space-time mapping technique based on linear algebra and linear programming. One can choose a parallel program that is optimal with respect to some objective function like the number of execution steps, processors, channels, etc. However,at best,linear execution time complexity can be atained. Through phrasing the polynomial product as a divide-and-conquer recursion, one can obtain a parallel program with sublinear execution time. In this case, the target program is not derived by an automatic search but given as a program skeleton, which can be deduced by a sequence of equational program transformations. We discuss the use of such skeletons, compare and assess the models in which loops and divide-and-conquer resursions are parallelized and comment on the performance properties of the resulting parallel implementations.

Architectural evaluation of a universal host computer munap

AbstractThis paper describes the architectural evaluation of a universal host computer MUNAP in terms of: (1) nonnumerical capability; (ii) multiprocessor parallelism; and (iii) flexibility of the two‐level microprogramming scheme, based on the experimental results.The findings of the dynamic evaluation are summarized as follows.(i) The divide and concatenate unit is especially useful for decoding machine instructions and manipulating tags in high‐level language machines so that the number of execution steps is decreased 30–40 percent. The bit operation unit is useful for numerical processing which frequently utilizes priority encoding. This provides a reduction in execution steps of 15 percent. In the shuffle exchange network, 16, 32, and 48‐bit circular shifts and broadcasts are used effectively for data transfers between processor units and serial operations.(ii) The average numbers of active processor units are 3.6 ‐ 3.8 for such numerical computations as Fast Fourier Transform, and 2.1 to 2.5 for emulations of a wide variety of high‐level languages.(iii) In the two‐level microprogramming scheme, the allocation ratio of the nanoprogram memory increases due to word size optimization of nanoprogram memory so that 80 ‐ 90 percent of it is used for large‐scale microprograms.