In this work we extend the study of solution graphs and prove that for boolean formulas in a class called CPSS, all connected components are partial cubes of small dimension, a statement which was proved only for some cases in [Schwerdtfeger 2013]. In contrast, we show that general Schaefer formulas ... more >>>

It is well known that problems encoded with circuits or formulas generally gain an exponential complexity blow-up compared to their original complexity.

We introduce a new way for encoding graph problems, based on $\textrm{CNF}$ or $\textrm{DNF}$ formulas. We show that contrary to the other existing succinct models, there are ... more >>>

We give a \#SAT algorithm for boolean formulas over arbitrary finite bases. Let $B_k$ be the basis composed of all boolean functions on at most $k$ inputs. For $B_k$-formulas on $n$ inputs of size $cn$, our algorithm runs in time $2^{n(1-\delta_{c,k})}$ for $\delta_{c,k} = c^{-O(c^2k2^k)}$. We also show the average-case ... more >>>