System-level diagnosis is a very important technique for identifying faulty processors in a system with a large number of processors. Processors can test other processors, and then output the test results. The aim of diagnosis is to determine correctly the faulty/fault-free status of all processors. The adaptive diagnosis have been studied in order to perform diagnosis more efficiently. In this paper, we present adaptive diagnosis algorithms for a system modeled by butterfly networks. Our algorithms identify all faulty nodes in butterfly networks with the optimal number of tests. Then, we design another algorithm for diagnosis with very small constant number of rounds.

We consider diagnosability of butterfly networks under the comparison approach proposed by Maeng and Malek. Sengupta and Dahbura discussed characterization of diagnosable systems under the comparison approach, and designed a polynomial time algorithm to identify the faulty processors. However, for a general system, it is not algorithmically easy to determine its diagnosability. This paper proposes two comparison schemes for generating syndromes on butterfly networks, and determine the diagnosability of the network.

In this paper, we study system-level diagnosis under the comparison approach proposed by Maeng and Malek. Sengupta and Dahbura designed an O(n5) time diagnosis algorithm for identifying all faulty nodes in general graphs (n is the number of nodes in a system). We consider diagnosis on a butterfly network BF(k,r) and propose O(k2 n) time diagnosis algorithms for locating all faulty nodes in BF(k,r).

A number of parallel algorithms have been developed to solve large-scale real world problems. Although there has been much work on the design of parallel algorithms, there has been little on the design of languages for expressing these algorithms. This paper describes the BPL, a new parallel language designed for butterfly networks. The purpose of this language is to help designers in hiding the complexity of the algorithm and leaving details of mapping between data and processors for lower level. BPL provides a simpler virtual machine for the designer , in order to avoid thinking about control of processors and data. From another point of view, BPL helps designer to logically check the algorithm and correct any possible error in it. The paper gives some examples implemented by this language. In addition, we have also implemented a software tool which simulates the running of the algorithm on the network. The results lead us to believe that this language would be useful in representing all kinds of algorithms on this network including normal algorithms and others.