Author:
Stanford Caleb,Veanes Margus
Abstract
AbstractIdentifying live and dead states in an abstract transition system is a recurring problem in formal verification; for example, it arises in our recent work on efficiently deciding regex constraints in SMT. However, state-of-the-art graph algorithms for maintaining reachability information incrementally (that is, as states are visited and before the entire state space is explored) assume that new edges can be added from any state at any time, whereas in many applications, outgoing edges are added from each state as it is explored. To formalize the latter situation, we propose guided incremental digraphs (GIDs), incremental graphs which support labeling closed states (states which will not receive further outgoing edges). Our main result is that dead state detection in GIDs is solvable in $$O(\log m)$$ amortized time per edge for m edges, improving upon $$O(\sqrt{m})$$ per edge due to Bender, Fineman, Gilbert, and Tarjan (BFGT) for general incremental directed graphs.We introduce two algorithms for GIDs: one establishing the logarithmic time bound, and a second algorithm to explore a lazy heuristics-based approach. To enable an apples-to-apples experimental comparison, we implemented both algorithms, two simpler baselines, and the state-of-the-art BFGT baseline using a common directed graph interface in Rust. Our evaluation shows 110-530x speedups over BFGT for the largest input graphs over a range of graph classes, random graphs, and graphs arising from regex benchmarks.
Publisher
Springer Nature Switzerland
Reference67 articles.
1. Abboud, A., Williams, V.V.: Popular conjectures imply strong lower bounds for dynamic problems. In: 2014 IEEE 55th Annual Symposium on Foundations of Computer Science, pp. 434–443. IEEE (2014)
2. Almeida, M., Moreira, N., Reis, R.: On the performance of automata minimization algorithms. Tech. Rep. DCC-2007-03, University of Porto (2007)
3. Alstrup, S., Holm, J., Lichtenberg, K.D., Thorup, M.: Maintaining information in fully dynamic trees with top trees. Acm Trans. Algorithms (talg) 1(2), 243–264 (2005)
4. Amadini, R.: A survey on string constraint solving. ACM Comput. Surv. (CSUR) 55(1), 1–38 (2021)
5. Antimirov, V.: Partial derivatives of regular expressions and finite automata constructions. Theoret. Comput. Sci. 155, 291–319 (1995)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献