Instruction Set and Language for Hypergraphs

The paper introduces IsalHG, an instruction language and virtual machine that serializes finite connected hypergraphs with bounded hyperedge arity into strings. A greedy encoder provides round trips, while a backtracking procedure attempts to produce a canonical string whose equality would decide hypergraph isomorphism directly. Tests cover 150 connected random uniform hypergraphs and named combinatorial designs. Across 600 verdicts, IsalHG agrees with nauty, Traces, and bliss applied to 2-coloured Levi graphs. However, the canonical-completeness claim remains a conjecture, and the proposed method is measured as 311x to 117,672x slower than the baselines.