Incremental Dead State Detection in Logarithmic Time

Abstract Identifying live and dead states in an abstract transition system is a recurring problem formal verification; for example, it arises our recent work on efficiently deciding regex constraints SMT. However, state-of-the-art graph algorithms maintaining reachability information incrementally (that is, as are visited before the entire state space explored) assume that new edges can be added from any at time, whereas many applications, outgoing each explored. To formalize latter situation, we propose guided incremental digraphs (GIDs), graphs which support labeling closed (states will not receive further edges). Our main result detection GIDs solvable $$O(\log m)$$ O ( log m ) amortized time per edge m edges, improving upon $$O(\sqrt{m})$$ due to Bender, Fineman, Gilbert, Tarjan (BFGT) general directed graphs. We introduce two GIDs: one establishing logarithmic bound, second algorithm explore lazy heuristics-based approach. enable apples-to-apples experimental comparison, implemented both algorithms, simpler baselines, BFGT baseline using common interface Rust. evaluation shows 110-530x speedups over largest input range of classes, random graphs, arising benchmarks.