Heribert Vollmer

We study the complexity of the following algorithmic problem: Given a Boolean function $f$ and a finite set of Boolean functions $B$, decide if there is a circuit with basis $B$ that computes $f$. We show that if both $f$ and all functions in $B$ are given by their truth-table, ... more >>>

Ruiwen Chen, Valentine Kabanets

We revisit the gate elimination method, generalize it to prove correlation bounds of boolean circuits with Parity, and also derive deterministic #SAT algorithms for small linear-size circuits. In particular, we prove that, for boolean circuits of size $3n - n^{0.51}$, the correlation with Parity is at most $2^{-n^{\Omega(1)}}$, and there ... more >>>

Andrzej Lingas

We consider normalized Boolean circuits that use binary operations of disjunction and conjunction, and unary negation, with the restriction that negation can be only applied to input variables. We derive a lower bound trade-off between the size of normalized Boolean circuits computing Boolean semi-disjoint bilinear forms and their conjunction-depth (i.e., ... more >>>

Stasys Jukna, Andrzej Lingas

We consider Boolean circuits over $\{\lor,\land,\neg\}$ with negations applied only to input variables. To measure the ``amount of negation'' in such circuits, we introduce the concept of their ``negation width.'' In particular, a circuit computing a monotone Boolean function $f(x_1,\ldots,x_n)$ has negation width $w$ if no nonzero term produced (purely ... more >>>