We present a way to abstract functional units in symbolic simulation of actual circuits, thus achieving the effect of uninterpreted functions at the bit-level. Additionally, we propose an efficient encoding technique that can be used to represent uninterpreted symbols with BDDs, while allowing these symbols to be propagated by simulation with a conventional bit-level symbolic simulator. Our abstraction and encoding techniques result in an automatic symmetry reduction and allow the control and forwarding logic of the actual circuit to be used unmodified. The abstraction method builds on the behavioral Efficient Memory Model [18] [19] and its capability to dynamically introduce consistent initial state, which is identical for two simulation sequences. We apply the abstraction and encoding ideas on the verification of pipelined microprocessors by correspondence checking, where a pipelined microproc...

Loop pipelining is a critical transformation in behavioral synthesis. It is crucial to producing hardware designs with acceptable latency and throughput. However, it is a complex transformation involving aggressive scheduling strategies for high throughput and careful control generation to eliminate hazards. We present an equivalence checking approach for certifying synthesized hardware designs in the presence of pipelining transformations. Our approach works by (1) constructing a provably correct pipeline reference model from sequential specification, and (2) applying sequential equivalence checking between this reference model and synthesized RTL. We demonstrate the scalability of our approach on several synthesized designs from a commercial synthesis tool.

Symbolic simulation is a formal verification technique which combines the flexibility of conventional simulation with powerful symbolic methods. Some constructs, however, which are easy to handle in conventional simulation need special consideration in symbolic simulation. This paper discusses some special constructs that require unique treatment in symbolic simulation such as the symbolic representation of arrays, an efficient symbolic method for storing arrayed instances and the handling of symbolic data-dependent delays. We present results which demonstrate the effectiveness of our symbolic array model in the simulation of highly regular structures like FPGAs, memories or cellular automata.