Matching is a central problem in theoretical computer science, with a large body of work spanning the last five decades. However, understanding matching in the time-space bounded setting remains a longstanding open question, even in the presence of additional resources such as randomness or non-determinism.

In this work we study ... more >>>

We initiate the study of complexity classes ${A^B}$ where ${A}$ and ${B}$ are both ${TFNP}$ subclasses. For example, we consider complexity classes of the form ${PPP^{PPP}}$, ${PPAD^{PPA}}$, and ${PPA^{PLS}}$. We define complete problems for such classes, and show that they belong in ${TFNP}$. These definitions require some care, since ... more >>>