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We consider satisfiable Tseitin formulas TSG,c based on d-regular expanders G with the absolute value of the second largest eigenvalue less than d3 . We prove that any nondeterministic read-once branching program (1-NBP) representing TSG,c has size 2(n), where n is the number of vertices in G. It extends the recent result by Itsykson at el. [9] from OBDD to 1-NBP. On the other hand it is easy to see that TSG,c can be represented as a read-2 branching program (2-BP) of size O(n), as the negation of a nondeterministic read-once branching program (1-coNBP) of size O(n) and as a CNF formula of size O(n). Thus TSG,c gives the best possible separations (up to a constant in the exponent) between 1-NBP and 2-BP, 1-NBP and 1-coNBP and between 1-NBP and CNF.
Original language | English |
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Title of host publication | 42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017 |
Editors | Kim G. Larsen, Jean-Francois Raskin, Hans L. Bodlaender |
Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
ISBN (Electronic) | 9783959770460 |
DOIs | |
State | Published - 1 Nov 2017 |
Event | 42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017 - Aalborg, Denmark Duration: 21 Aug 2017 → 25 Aug 2017 |
Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 83 |
ISSN (Print) | 1868-8969 |
Conference | 42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017 |
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Country/Territory | Denmark |
City | Aalborg |
Period | 21/08/17 → 25/08/17 |
ID: 49785281