Using fixed-point semantics to prove retiming lemmas
Formal Methods in System Design
The validity of retiming sequential circuits
DAC '95 Proceedings of the 32nd annual ACM/IEEE Design Automation Conference
The retiming lemma: a simple proof and applications
Integration, the VLSI Journal
Behavior and testability preservation under the retiming transformation
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
On some transformation invariants under retiming and resynthesis
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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We propose a novel approach to preserve the synchronizing sequences of a circuit after retiming. The significance of this problem stems from the necessity of maintaining correct initialization of circuits after retiming optimizations. It has been previously shown that forward retiming moves across fanout stems can destroy a synchronizing sequence. We build on this observation and introduce the notion of "invalid states" that might arise due to forward moves. We show that the set of synchronizing sequences of a given circuit can be preserved by modifying transitions from those invalid states. We present an algorithm that implicitly computes the set of invalid states. Then, we describe a post-retiming synthesis step that incrementally resynthesizes some next-state functions to alter the behavior of invalid states to ensure correct post-retiming initialization. We report promising experimental results on the ISCAS 89 benchmarks and on a set of retimed circuits from an Intel Pentium-III class microprocessor.