Two-hybrid methods have augmented the classical genetic techniques biologists use to assign function to genes. Here, we describe construction of a two-bait interaction trap that uses yeast cells to register more complex protein relationships than those detected in existing two-hybrid systems. We show that such cells can identify bridge or connecting proteins and peptide aptamers that discriminate between closely related allelic variants. The protein relationships detected by these cells are analogous to classical genetic relationships, but lend themselves to systematic application to the products of entire genomes and combinatorial libraries. We show that, by performing logical operations on the phenotypic outputs of these complex cells and existing two-hybrid cells, we can make inferences about the topology and order of protein interactions. Finally, we show that cells that register such relationships can perform logical operations on protein inputs. Thus these cells will be useful for analysis of gene and allele function, and may also define a path for construction of biological computational devices.