Incremental Methods for Formal Verification and Logic Synthesis

Abstract

IC design is an iterative process; the initial specification of a design is rarely complete and correct. The designer begins with a preliminary and usually incorrect sketch (possibly from a previous generation design), and iteratively refines and corrects it. Usually, refinements are small, and there is much common information between successive design iterations. The current genre of CAD tools do not take into account this iterative nature of design. For each change made to the design, the design is re-verified and re-optimized without taking advantage of information from previous iterations. This leads to inefficient performance. In this thesis, we propose the paradigm of incremental algorithms for CAD. Incremental algorithms use information from a previous design iteration, as well as information about changes to the design to evaluate the design efficiently. In particular, we examine incremental algorithms for two different classes of CAD problems: formal design verification and logic synthesis. Design verification is the process of checking if the design satisfies all the initial specifications. Most existing techniques for verification evaluate the entire design in a single pass. In practice design verification is never called just once; the designer tends to modify the system both iteratively and incrementally, and would like to incrementally call the verifier at each stage. Current techniques ignore this common information. This redundancy is particularly costly while dealing with large systems that take a lot of time and effort to verify. This thesis proposes incremental formal design verification as a solution to this problem. Incremental verification runs the entire verification process only once, and propagates successive changes or increments thereafter. We have developed incremental algorithms for the two most commonly used methods for formal design verification: language containment and model checking. Logic synthesis refers to the process of optimizing a logic description of a circuit, specified as a netlist of logic gates. This representation can be optimized for area, delay, and power. Most problems in logic synthesis are computationally hard, and are solved using heuristics. This often makes algorithms unstable; if the input is changed slightly, the new result of synthesis can be significantly different. Since a designer can spend much effort hand-optimizing circuits, it is desirable to retain as much of this human insight as possible. In addition, the network may have already been implemented in silicon at a lower level of the design hierarchy, and it can be inconvenient to change. We propose the paradigm of incremental synthesis, whose underlying motivation is to preserve the old design implementation, while keeping the objective (power, area, delay) reasonable. In incremental verification, it is imperative to get exactly the same answer as by running non-incremental verification; incrementalization saves the designer computation effort and time by utilizing information from previous iterations. However, an incremental synthesis algorithm is concerned more with preserving similarity to the earlier design, and hence is not guaranteed to have the same result as the corresponding non-incremental algorithm. The paradigm of incremental analysis, in both synthesis and verification, raises issues of detecting change from a new high-level specification of the design. We present methods for detecting changes made to the system from a high-level specification of the design. The final overall goal of this thesis is create incremental algorithms for CAD, and to demonstrate their effectiveness to the user.