On the Fine Grained Complexity of Finite Automata Non-emptiness of Intersection [chapter]

Mateus de Oliveira Oliveira, Michael Wehar
2020 Lecture Notes in Computer Science  
We study the fine grained complexity of the DFA nonemptiness of intersection problem parameterized by the number k of input automata (k-DFA-NEI). More specifically, we are given a list A1, ..., A k of DFA's over a common alphabet Σ, and the goal is to determine whether k i=1 L(Ai) = ∅. This problem can be solved in time O(n k ) by applying the classic Rabin-Scott product construction. In this work, we show that the existence of algorithms solving k-DFA-NEI in time slightly faster than O(n k )
more » ... uld imply the existence of deterministic sub-exponential time algorithms for the simulation of nondeterministic linear space bounded computations. This consequence strengthens the existing conditional lower bounds for k-DFA-NEI and implies new non-uniform circuit lower bounds.
doi:10.1007/978-3-030-48516-0_6 fatcat:ixsbtp5aereifa7yn5hv5gqvne