Formalization of Data Flow Computing and a Coinductive Approach to Verifying Flowware Synthesis

Reconfigurable computing refers to the notions of

configware

and

flowware

. Configware means structural programming, or programming in space to execute computation in space. Flowware means data-flow programming that schedules the data flow for output from or input to the configware architecture. In this paper, data flows of a synthesized computation are formalized. This means that data flow is specified as a behavioral stream function in stream calculus, which is used to underpin the semantics for Register Transfer Level (RTL) synthesis. A stream representation allows the use of coinductive principles in stream calculus. In particular, using the coinductive proof principle, we show that behavioral stream functions in the three-stage synthesis process (scheduling, register allocation and binding, allocation and binding of functional units) are always bisimilar regardless of changes in a scheduling, allocation or binding procedure. Our formalization makes pipelining possible, in which all functional units as well as registers of hardware resources are reused during different control steps (C-steps). Moreover, a coinductive approach to verifying flowware synthesis, which is independent of the heuristic during register allocating and binding step, is proposed as a practical technique.