The concept of redundancy in SAT lead to more expressive and powerful proof search techniques, e.g. able to express various inprocessing techniques, and to interesting hierarchies of proof systems [Heule et.al’20, Buss-Thapen’19].
We propose a general way to integrate redundancy rules in MaxSAT, that is we define MaxSAT variants of ... more >>>

Regular resolution is a refinement of the resolution proof system requiring that no variable be resolved on more than once along any path in the proof. It is known that there exist sequences of formulas that require exponential-size proofs in regular resolution while admitting polynomial-size proofs in resolution. Thus, with ... more >>>

We describe CNFs in n variables which, over a range of parameters, have small resolution refutations but are such that any small refutation must have height larger than n (even exponential in n), where the height of a refutation is the length of the longest path in it. This is ... more >>>

Connections between proof complexity and circuit complexity have become major tools for obtaining lower bounds in both areas. These connections -- which take the form of interpolation theorems and query-to-communication lifting theorems -- translate efficient proofs into small circuits, and vice versa, allowing tools from one area to be applied ... more >>>

This paper is motivated by seeking lower bounds on OBDD($\land$, weakening, reordering) refutations, namely OBDD refutations that allow weakening and arbitrary reorderings. We first work with 1-NBP($\land$) refutations based on read-once nondeterministic branching programs. These generalize OBDD($\land$, reordering) refutations. There are polynomial size 1-NBP($\land$) refutations of the pigeonhole principle, hence ... more >>>

Atserias, Kolaitis, and Vardi [AKV04] showed that the proof system of Ordered Binary Decision Diagrams with conjunction and weakening, OBDD($\land$, weakening), simulates CP* (Cutting Planes with unary coefficients). We show that OBDD($\land$, weakening) can give exponentially shorter proofs than dag-like cutting planes. This is proved by showing that the Clique-Coloring ... more >>>

We give a combinatorial analysis (using edge expansion) of a variant of the iterative expander construction due to Reingold, Vadhan, and Wigderson [Annals of Mathematics, 2002], and show that this analysis can be formalized in the bounded-arithmetic system $VNC^1$ (corresponding to the ``$NC^1$ reasoning''). As a corollary, we prove the ... more >>>

The 2-D Tucker search problem is shown to be PPA-hard under many-one reductions; therefore it is complete for PPA. The same holds for $k$-D Tucker for all $k\ge 2$. This corrects a claim in the literature that the Tucker search problem is in PPAD.

This paper characterizes alternation trading based proofs that satisfiability is not in the time and space bounded class $\DTISP(n^c, n^\epsilon)$, for various values $c<2$ and $\epsilon<1$. We characterize exactly what can be proved in the $\epsilon=0$ case with currently known methods, and prove the conjecture of Williams that $c=2\cos(\pi/7)$ is ... more >>>