A Complete Enumeration of Ternary Logic Gate Functions

This dataset contains the complete enumeration of ternary logic gates, a total of 3774 gates, where each gate is represented as a discrete function mapping inputs from {-1, 0, +1} to outputs in {-1, 0, +1}. The dataset was generated through an exhaustive computational sweep over the ternary function space, ensuring that all possible gate configurations within the defined input domain are included. The enumeration process was implemented in C++, where each candidate function was constructed and evaluated over the full input space. For a given arity (e.g., unary or binary), all possible input combinations were systematically iterated, and corresponding output assignments were generated. The resulting gates were optionally filtered or grouped using isomorphism-aware transformations, including permutations of input variables and value relabeling, to support structural analysis and reduction of equivalent classes. Each gate in the dataset is encoded as a sequence of symbols from the set {+, -, 0}, representing output values for ordered input combinations. The encoding follows a lexicographic ordering of inputs, where + -> +1, 0 -> 0, and - -> -1. For decoding, enumerate all input tuples in lexicographic order over {-1, 0, +1} and map each symbol in the sequence to its corresponding numeric value. For example, in the unary case, the input ordering is [-1, 0, +1], and a gate encoded as +0- corresponds to f(-1)=+1, f(0)=0, and f(+1)=-1. In the binary case, the input ordering follows (-1,-1), (-1,0), (-1,+1), (0,-1), (0,0), (0,+1), (+1,-1), (+1,0), (+1,+1). This dataset is intended to support research in multi-valued logic, ternary computation, universality analysis, and logic synthesis, and is accompanied by code to reproduce the enumeration process.