Boolean Matching Reversible Circuits: Algorithm and Complexity
arxiv(2024)
摘要
Boolean matching is an important problem in logic synthesis and verification.
Despite being well-studied for conventional Boolean circuits, its treatment for
reversible logic circuits remains largely, if not completely, missing. This
work provides the first such study. Given two (black-box) reversible logic
circuits that are promised to be matchable, we check their equivalences under
various input/output negation and permutation conditions subject to the
availability/unavailability of their inverse circuits. Notably, among other
results, we show that the equivalence up to input negation and permutation is
solvable in quantum polynomial time, while its classical complexity is
exponential. This result is arguably the first demonstration of quantum
exponential speedup in solving design automation problems. Also, as a negative
result, we show that the equivalence up to both input and output negations is
not solvable in quantum polynomial time unless UNIQUE-SAT is, which is
unlikely. This work paves the theoretical foundation of Boolean matching
reversible circuits for potential applications, e.g., in quantum circuit
synthesis.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要