Approximate timing analysis of combinational circuits under the XBDO model

Abstract

This paper is concerned with approximate delay computation algorithms for combinational circuits. As a result of intensive research in the early 90's efficient tools exist which can analyze circuits of thousands of gates in a few minutes or even in seconds for many cases. However, the computation time of these tools is not so predictable since the internal engine of the analysis is either a SAT solver or a modified ATPG algorithm, both of which are just heuristic algorithms for an NP-complete problem. Although they are highly tuned for CAD applications, there exists a class of problem instances which exhibits the worst-case exponential CPU time behavior. In the context of timing analysis, circuits with a high amount of reconvergence, e.g. C6288 of the ISCAS benchmark suite, are known to be difficult to analyze under sophisticated delay models even with state-of-the-art techniques. To make timing analysis of such corner case circuits feasible we propose an approximate computation scheme to the timing analysis problem as an extension to the exact analysis method proposed previously. Sensitization conditions are conservatively approximated in a selective fashion so that the size of SAT problems solved during analysis is controlled. Experimental results show that the approximation technique is effective in reducing the total analysis time without losing accuracy for the case where the exact approach takes much time or cannot complete.