CTT Algorithm

CTT Project - Hwang Joon This paper was written using OpenAI's GPT-5.6sol model, which successfully created a practical and groundbreaking SAT solver. The list of SAT subclasses that are theoretically solvable in polynomial time is as follows. 2-SAT/Bijunctive SAT, Horn-SAT, Dual-Horn-SAT, Affine-SAT/XOR-SAT, 0-valid Boolean CSP, 1-valid Boolean CSP, Renamable Horn-SAT, q-Horn SAT, β-acyclic SAT, α-acyclic/acyclic CSP, bounded-treewidth SAT, bounded-incidence-treewidth SAT, bounded-primal-treewidth SAT, bounded-hypertree-width CSP, bounded-fractional-hypertree-width CSP, constant-size strong 2-SAT backdoor SAT, constant-size Horn backdoor SAT, constant-size Affine/XOR backdoor SAT, Clique on perfect graphs, Maximum Independent Set on perfect graphs, Graph Coloring on perfect graphs, Clique on chordal graphs, Independent Set on chordal graphs, Coloring on chordal graphs, Clique on interval graphs, Independent Set on interval graphs, Coloring on interval graphs, Independent Set on bipartite graphs, Vertex Cover on bipartite graphs, Clique on bipartite graphs, Coloring on bipartite graphs, Bipartite Vertex Cover, Bipartite Matching, Assignment Problem, Weighted Bipartite Matching, b-Matching, network-flow reducible matching subclasses, Hamiltonian Path on DAGs, Hamiltonian Path on tournaments, Hamiltonian Cycle on strongly connected tournaments, Hamiltonian problems on bounded-treewidth graphs, interval/permutation-graph restricted Hamiltonian subclasses, Max-Cut on bipartite graphs, Planar Max-Cut, Max-Cut on bounded-treewidth graphs, Dominating Set on interval graphs, Dominating Set on permutation graphs, Dominating Set on bounded-treewidth graphs, Set Cover on laminar set systems, interval/set-system covering subclasses, TSP on trees, TSP on bounded-treewidth graphs, TSP on bounded-pathwidth graphs, Kalmanson-matrix TSP, Demidenko-matrix TSP, Monge TSP subclasses, Pyramidal TSP, Unary Subset Sum, Unary Knapsack, Unary Partition, polynomially bounded-capacity Knapsack, polynomially bounded-target Subset Sum, Fixed-dimensional Integer Programming, Difference Constraints, Network Matrix ILP, Totally Unimodular ILP, flow/circulation formulations, bipartite-matching polytope classes, Acyclic CSP, Bounded-treewidth CSP, Bounded-hypertree-width CSP, Bounded fractional hypertree-width CSP, Horn CSP, Bijunctive CSP, Affine CSP, Maltsev-type tractable CSP classes, Bounded-width CSP classes, Majority-polymorphism classes, Semilattice-polymorphism classes, Equality/Disequality SAT, Parity-DSU systems, Pure One-Hot Matching, Bipartite Perfect Matching, Sequential-counter one-hot after recovery, Guarded parity systems with polynomial guard elimination, Guarded equality systems reducible to parity-DSU, Arithmetic/miter subclasses reducible to exact functional equivalence. This project encompasses everything from genetic lineage reconstruction using CTT to LLM analysis. In accordance with the laws and educational guidelines of the Republic of Korea, the author's affiliation (as of September 9, 2026) is specified. Powiis penang.