The Polynomial Hierarchy in communication complexity as defined by Babai, Frankl, and Simon (see the original paper here and without the paywall here). The significance of this hierarchy is hard to overestimate. First of all, the disjointness function was introduced by BFS in the same paper that introduced the hierarchy, and the disjointness appeared quite naturally as a coNP$^{cc}$-complete problem. As you know, the disjointness is THE function in communication complexity. Secondly, proving lower bounds against the polynomial hierarchy in communication complexity is a major open problem with important implications in other areas of TCS (for example, see this paper and references therein).
The Polynomial Hierarchy in communication complexity as defined by Babai, Frankl, and Simon (see the original paper here and without the paywall here). The significance of this hierarchy is hard to overestimate. First of all, the disjointness function was introduced by BFS in the same paper that introduced the hierarchy, and the disjointness appeared quite naturally as a coNP-complete problem. As you know, the disjointness is THE function in communication complexity. Secondly, proving lower bounds against the polynomial hierarchy in communication complexity is a major open problem with important implications in other areas of TCS (for example, see this paper and references therein).
The Polynomial Hierarchy in communication complexity as defined by Babai, Frankl, and Simon (see the original paper here and without the paywall here). The significance of this hierarchy is hard to overestimate. First of all, the disjointness function was introduced by BFS in the same paper that introduced the hierarchy, and the disjointness appeared quite naturally as a coNP$^{cc}$-complete problem. As you know, the disjointness is THE function in communication complexity. Secondly, proving lower bounds against the polynomial hierarchy in communication complexity is a major open problem with important implications in other areas of TCS (for example, see this paper and references therein).
The Polynomial Hierarchy in communication complexity as defined by Babai, Frankl, and Simon (see the original paper here and without the paywall here). The significance of this hierarchy is hard to overestimate. First of all, the disjointness function was introduced by BFS in the same paper that introduced the hierarchy, and the disjointness appeared quite naturally as a coNP-complete problem. As you know, the disjointness is THE function in communication complexity. Secondly, proving lower bounds against the polynomial hierarchy in communication complexity is a major open problem with important implications in other areas of TCS (for example, see this paper and references therein).