A classification for commutative three-element semigroups with local XOR structure and its implementability of card-based protocols
Yuji Suga · 2023
Based on the 2-party XOR protocols, we consider an extended protocol that allows the input of a third value "indeterminate" which is neither 0 nor 1. Assuming only algebraic structures that satisfy the associative law, we classify patterns that can be constructed as boolean tables, and report on the feasibility of implementing the protocol as card protocols.