eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-12-01
26:1
26:12
10.4230/LIPIcs.MFCS.2017.26
article
Satisfiable Tseitin Formulas Are Hard for Nondeterministic Read-Once Branching Programs
Glinskih, Ludmila
Itsykson, Dmitry
We consider satisfiable Tseitin formulas TS_{G,c} based on d-regular expanders G with the absolute value of the second largest eigenvalue less than d/3. We prove that any nondeterministic read-once branching program (1-NBP) representing TS_{G,c} has size 2^{\Omega(n)}, where n is the number of vertices in G. It extends the recent result by Itsykson at el. [STACS 2017] from OBDD to 1-NBP.
On the other hand it is easy to see that TS_{G,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 TS_{G,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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol083-mfcs2017/LIPIcs.MFCS.2017.26/LIPIcs.MFCS.2017.26.pdf
Tseitin formula
read-once branching program
expander