A unified model of pointwise equivalence of procedural computations

Reviewer: R. Sambasiva Rao

The migration of an executing process from one machine to a different one where it is to be executed is a fascinating and challenging task. A source program in any high-level language is compiled, and it runs on a processor under an operating system. The execution of each instruction produces a change in the state. Thus, the program's execution on a processor is modeled as a sequence of states. Hence, process migration requires cooperation between the operating systems, application, and language. In earlier work on heterogeneous migration, the migrating program is suspended. Then a copy of the state is transferred to a target or destination machine, and the run is continued. The disadvantage of this approach is the extra work required to gather the information regarding the state of the process, which is distributed between the address space and CPU registers. In one approach, the compiler is modified to generate a code for all expected target machines along with the necessary migration information. Another attempt was to dynamically construct a machine development program representing the state of computation at the time of migration. This program is compiled on the destination machine and then run to continue the migrated process. In a third approach, the debugger information is used to build a machine-independent form of the process. It is transferred to the target machine, where it is converted to the target machine's architecture, and the execution is continued. This paper adopts the concept of finding pointwise equivalents in the computation where it is possible to transfer the code between the two machines. Considering a process with initial state SA 0 ,SB 0 and final state SA n ,SB m on two machines of different architectures, naturally there will be different intermediate steps. This contribution aims at identifying the existence and nature of the points of equivalence in a hypothetical process coded in C. The program reads a matrix of integers, sorts the columns, and displays the sorted matrix. The authors assume that the architecture of one machine is such that it implements access to array elements by placing an offset in a register, and uses address modifications with indexing access to the element. The other machine takes the array elements by using address arithmetic to place a pointer into a register, and then it employs dereferencing to access the element. The authors anticipate a straightforward extension of pointwise equivalence to an arbitrary number of instances of computation. A modern, retargetable language needs modification to incorporate the model of pointwise equivalence while generating the object code. Furthermore , it should incorporate transformation information for different target machines.