On complementing unambiguous automata and graphs with many cliques and cocliques
We show that for any unambiguous finite automaton with n states there exists an unambiguous finite automaton with √n + 1 · 2n/2 states that recognizes the complement language. This builds and improves upon a similar result by Jirásek et al. (2018) [1]. Our improvement is based on a reduction to and...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Elsevier
2022
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| Summary: | We show that for any unambiguous finite automaton with n states there exists an unambiguous finite automaton with √n + 1 · 2n/2 states that recognizes the complement language. This builds and improves upon a similar result by Jirásek et al. (2018) [1]. Our improvement is based on a reduction to and an analysis of a problem from extremal graph theory: we show that for any graph with n vertices, the product of the number of its cliques with the number of its cocliques (independent sets) is bounded by (n + 1)2n. |
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