This note revisits the study of search problems that are solvable in probabilistic polynomial time. Previously, Goldreich (2011) introduced a class called ``$\mathcal{BPP}$-search'', and studied search-to-decision reductions for problems in this class.

In Goldreich's original formulation, the definition of what counts as ``successfully solving'' a $\mathcal{BPP}$-search problem is implicit, and ... more >>>

There has been tremendous progress in the past decade in the field of quantified Boolean formulas (QBF), both in practical solving as well as in creating a theory of corresponding proof systems and their proof complexity analysis. Both for solving and for proof complexity, it is important to have interesting ... more >>>

We propose a new definition of the class of search problems that correspond to BPP.
Specifically, a problem in this class is specified by a polynomial-time approximable function $q:\{0,1\}^*\times\{0,1\}^*\to[0,1]$ that associates, with each possible solution $y$ to an instance $x$, a quality $q(x,y)$.
Intuitively, quality 1 corresponds to perfectly ... more >>>