Improved reachability analysis on retiming of Dsp algorithms with an efficient cell enumeration method

Retiming is a very important technology to DSP because it can optimize hardware circuits by reallocating registers without affecting the function. When applying the DSP technology, marked graph is used as a model of computation, and retiming indeed is a transformation that changes the distribution of tokens on arcs in marked graph. The theoretical base for the retiming transformation is finding the set of functionally equivalent initial markings. This process is called reachability analysis. For this reason, reachability analysis is one of the most important problem on retiming of DSP. The reachability analysis in marked graph can be performed by finding a integer solution to a set of linear equation, which is known to be NP-complete. In this paper, a novel approach for finding the integer solution is introduced with a complexity bound of O((nu)^n-m), where n is the number of nodes, m is the number of arcs and u is the upper bound of the number of firings for all individual arcs. By reconstructing the marked graph that makes n - m equals to one, this algorithm can provide a very efficient approach to retiming of DSP.