We prove new exponential monotone circuit lower bounds for detecting perfect matchings. We show that $\exp(\widetilde{\Omega}(n^{1/2}))$ gates are required to detect bipartite perfect matchings in $n$-vertex graphs. Our lower bounds are based on a new spread matching lemma.

Eliminated lower order terms following suggestions made by Gaia Carenini and Yassine Ghannane.

We show that $\exp(\widetilde{\Omega}(n^{1/2}))$ gates are required to detect bipartite perfect matchings in $n$-vertex graphs. Our lower bounds are based on a new spread matching lemma.

Fixed an error in one of the proofs.

We show that $\exp(\widetilde{\Omega}(n^{1/2}))$ gates are required to detect bipartite perfect matchings in $n$-vertex graphs. Our lower bounds are based on a new spread matching lemma.

Fixed typos and changed notation

We prove new exponential monotone circuit lower bounds for detecting perfect matchings. We show that $\exp(\widetilde{\Omega}(n^{1/2}))$ gates are required to detect bipartite perfect matchings in $n$-vertex graphs. Our lower bounds are based on a new spread matching lemma.

Fixed some typos.

We prove new exponential monotone circuit lower bounds for detecting perfect matchings. We show that $\exp(\widetilde{\Omega}(n^{1/2}))$ gates are required to detect bipartite perfect matchings in $n$-vertex graphs. Our lower bounds are based on a new spread matching lemma.