Intersection Non-emptiness and Hardness Within Polynomial Time

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11088)


We establish strong connections between the non-emptiness of intersection problem for two and three DFA’s over a binary alphabet and the triangle finding and 3sum problems. In particular, we introduce efficient reductions from triangle finding to non-emptiness of intersection for two DFA’s over a binary alphabet and from 3sum to non-emptiness of intersection for three DFA’s over a binary alphabet. Additionally, in our main result, we show that for every \(\alpha \ge 2\), non-emptiness of intersection for three DFA’s over a unary alphabet can be solved in \(O(n^{\frac{\alpha }{2}})\) time if and only if triangle finding can be solved in \(O(n^{\alpha })\) time.


Intersection non-emptiness Computational complexity Unary automata 


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Authors and Affiliations

  1. 1.University of BergenBergenNorway
  2. 2.Temple UniversityPhiladelphiaUSA

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