Martin Sauerhoff

We extend the tools for proving lower bounds for randomized branching

programs by presenting a new technique for the read-once case which is

applicable to a large class of functions. This technique fills the gap

between simple methods only applicable for OBDDs and the well-known

"rectangle technique" of Borodin, Razborov ...
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Ludmila Glinskih, Dmitry Itsykson

We show that any nondeterministic read-once branching program that computes a satisfiable Tseitin formula based on an $n\times n$ grid graph has size at least $2^{\Omega(n)}$. Then using the Excluded Grid Theorem by Robertson and Seymour we show that for arbitrary graph $G(V,E)$ any nondeterministic read-once branching program that computes ... more >>>

Dmitry Itsykson, Artur Riazanov, Danil Sagunov, Petr Smirnov

We show that the size of any regular resolution refutation of Tseitin formula $T(G,c)$ based on a graph $G$ is at least $2^{\Omega(tw(G)/\log n)}$, where $n$ is the number of vertices in $G$ and $tw(G)$ is the treewidth of $G$. For constant degree graphs there is known upper bound $2^{O(tw(G))}$ ... more >>>

Xin Li, Yan Zhong

Affine extractors give some of the best-known lower bounds for various computational models, such as AC$^0$ circuits, parity decision trees, and general Boolean circuits. However, they are not known to give strong lower bounds for read-once branching programs (ROBPs). In a recent work, Gryaznov, Pudl\'{a}k, and Talebanfard (CCC' 22) introduced ... more >>>

Lijie Chen, William Hoza, Xin Lyu, Avishay Tal, Hongxun Wu

A weighted pseudorandom generator (WPRG) is a generalization of a pseudorandom generator (PRG) in which, roughly speaking, probabilities are replaced with weights that are permitted to be positive or negative. We present new explicit constructions of WPRGs that fool certain classes of standard-order read-once branching programs. In particular, our WPRGs ... more >>>