Prototyping time- and space-efficient computations of algebraic operations over dynamically reconfigurable systems modeled by rewriting-logic

Many algebraic operations can be efficiently implemented as pipe networks in arrays of functional units such as systolic arrays that provide a large amount of parallelism. However, the applicability of classical systolic arrays is restricted to problems with strictly regular data dependencies yielding only arrays with uniform linear pipes. This limitation can be circumvented by using reconfigurable systolic arrays or reconfigurable data path arrays, where the node interconnections and operations can be redefined even at run time. In this context, several alternative reconfigurable systolic architectures can be explored and powerful tools are needed to model and evaluate them. Well-known rewriting-logic environments such as ELAN and Maude can be used to specify and simulate complex application-specific integrated systems. In this article we propose a methodology based on rewriting-logic which is adequate to quickly model and evaluate reconfigurable architectures (RA) in general and, in particular, reconfigurable systolic architectures. As an interesting case study we apply this rewriting-logic modeling methodology to the space-efficient treatment of the Fast-Fourier Transform (FFT). The FFT prototype conceived in this way, has been specified and validated in VHDL using the Quartus II system.