Formal Verification Techniques for Reversible Circuits
Limaye, Chinmay Avinash
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As the number of transistors per unit chip area increases, the power dissipation of the chip becomes a bottleneck. New nano-technology materials have been proposed as viable alternatives to CMOS to tackle area and power issues. The power consumption can be minimized by the use of reversible logic instead of conventional combinational circuits. Theoretically, reversible circuits do not consume any power (or consume minimal power) when performing computations. This is achieved by avoiding information loss across the circuit. However, use of reversible circuits to implement digital logic requires development of new Electronic Design Automation techniques. Several approaches have been proposed and each method has its own pros and cons. This often results in multiple designs for the same function. Consequently, this demands research in efficient equivalence checking techniques for reversible circuits. This thesis explores the optimization and equivalence checking of reversible circuits. Most of the existing synthesis techniques work in two steps â generate an original, often sub-optimal, implementation for the circuit followed optimization of this design. This work proposes the use of Binary Decision Diagrams for optimization of reversible circuits. The proposed technique identifies repeated gate (trivial) as well as non-contiguous redundancies in a reversible circuit. Construction of a BDD for a sub-circuit (obtained by sliding a window of fixed size over the circuit) identifies redundant gates based upon the redundant variables in the BDD. This method was unsuccessful in identifying any additional redundancies in benchmark circuits; however, hidden non-contiguous redundancies were consistently identified for a family of randomly generated reversible circuits. As of now, several research groups focus upon efficient synthesis of reversible circuits. However, little work has been done in identification of redundant gates in existing designs and the proposed peephole optimization method stands among the few known techniques. This method fails to identify redundancies in a few cases indicating the complexity of the problem and the need for further research in this area. Even for simple logical functions, multiple circuit representations exist which exhibit a large variation in the total number of gates and circuit structure. It may be advantageous to have multiple implementations to provide flexibility in choice of implementation process but it is necessary to validate the functional equivalence of each such design. Equivalence checking for reversible circuits has been researched to some extent and a few pre-processing techniques have been proposed prior to this work. One such technique involves the use of Reversible Miter circuits followed by SAT-solvers to ascertain equivalence. The second half of this work focuses upon the application of the proposed reduction technique to Reversible Miter circuits as a pre-processing step to improve the efficiency of the subsequent SAT-based equivalence checking.
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