Towards practical FPRAS for #NFA: Exploiting the Power of Dependence
Kuldeep S. Meel, Alexis de Colnet

TL;DR
This paper introduces a new, more practical FPRAS algorithm for counting words accepted by an NFA, significantly reducing the time complexity and making it more feasible for real-world applications.
Contribution
The paper presents a novel FPRAS for #NFA with a substantially improved time complexity, approaching practical implementation.
Findings
New FPRAS with $O(n^2m^3 ext{log}(nm) ext{ε}^{-2} ext{log}( ext{δ}^{-1}))$ complexity
Achieves sub-quadratic complexity relative to membership checks
Marks progress towards practical approximation algorithms for #NFA
Abstract
#NFA refers to the problem of counting the words of length accepted by a non-deterministic finite automaton. #NFA is #P-hard, and although fully-polynomial-time randomized approximation schemes (FPRAS) exist, they are all impractical. The first FPRAS for #NFA had a running time of , where is the number of states in the automaton, is the confidence parameter, and is the tolerance parameter (typically smaller than ). The current best FPRAS achieved a significant improvement in the time complexity relative to the first FPRAS and obtained FPRAS with time complexity . The complexity of the improved FPRAS is still too intimidating to attempt any practical implementation. In this paper, we pursue the quest for practical…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComplexity and Algorithms in Graphs · Markov Chains and Monte Carlo Methods · Ferroelectric and Negative Capacitance Devices
