From Width-Based Model Checking to Width-Based Automated Theorem Proving

In the field of parameterized complexity theory, study graph width measures has been intimately connected with development width-based model checking algorithms for combinatorial properties on graphs. this work, we introduce a general framework to convert large class model-checking into that can be used test validity graph-theoretic conjectures classes graphs bounded width. Our is modular and applied respect several well-studied graphs, including treewidth cliquewidth. As quantitative application our framework, prove analytically long-standing conjectures, there exists an algorithm takes number k as input correctly determines in time double-exponential polynomial whether conjecture valid all at most k. These upper bounds, which may regarded upper-bounds size proofs/disproofs these k, improve significantly theoretical bounds obtained using previously available techniques.