Related papers: Width and size of regular resolution proofs
For any unsatisfiable CNF formula we give an exponential lower bound on the size of resolution refutations of a propositional statement that the formula has a resolution refutation. We describe three applications. (1) An open question in…
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…
Various "hardness" measures have been studied for resolution, providing theoretical insight into the proof complexity of resolution and its fragments, as well as explanations for the hardness of instances in SAT solving. In this report we…
It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…
In this paper we prove lower bounds for sizes of refutations of unsatisfiable vector Subset Sum instances $\overrightarrow{a}_1 x_1 + \dots + \overrightarrow{a}_n x_n = \overrightarrow{b}$ in the proof system Res(lin$_{\mathbb{F}_q}$) where…
We investigate the size complexity of proofs in $Res(s)$ -- an extension of Resolution working on $s$-DNFs instead of clauses -- for families of contradictions given in the {\em unusual binary} encoding. A motivation of our work is size…
We prove that there are 3-CNF formulas over n variables that can be refuted in resolution in width w but require resolution proofs of size n^Omega(w). This shows that the simple counting argument that any formula refutable in width w must…
This work is a survey on completely regular codes. Known properties, relations with other combinatorial structures and constructions are stated. The existence problem is also discussed and known results for some particular cases are…
Tseitin-formulas are systems of parity constraints whose structure is described by a graph. These formulas have been studied extensively in proof complexity as hard instances in many proof systems. In this paper, we prove that a class of…
This paper is devoted to dimensional reductions via the norm resolvent convergence. We derive explicit bounds on the resolvent difference as well as spectral asymptotics. The efficiency of our abstract tool is demonstrated by its…
We show that there are CNF formulas which can be refuted in resolution in both small space and small width, but for which any small-width proof must have space exceeding by far the linear worst-case upper bound. This significantly…
Resolution over linear equations is a natural extension of the popular resolution refutation system, augmented with the ability to carry out basic counting. Denoted Res(lin_R), this refutation system operates with disjunctions of linear…
The mean width of a convex body is the average distance between parallel supporting hyperplanes when the normal direction is chosen uniformly over the sphere. The Simplex Mean Width Conjecture (SMWC) is a longstanding open problem that says…
In this short note we explain how to construct resolutions or regular alterations admitting an ample exceptional divisor, assuming the existence of projective resolutions or regular alterations. In particular, this implies the existence of…
It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the…
The Stone tautologies are known to have polynomial size resolution refutations and require exponential size regular refutations. We prove that the Stone tautologies also have polynomial size proofs in both pool resolution and the proof…
In this paper, we discuss necessary and sufficient explanations for formal argumentation - the question whether and why a certain argument can be accepted (or not) under various extension-based semantics. Given a framework with which…
We prove two results about width of words in $SL_n(\mathbb{Z})$. The first is that, for every $n \geq 3$, there is a constant $C(n)$ such that the width of any word in $SL_n(\mathbb{Z})$ is less than $C(n)$. The second result is that, for…
A superredundant clause is a clause that is redundant in the resolution closure of a formula. The converse concept of superirredundancy ensures membership of the clause in all minimal CNF formulae that are equivalent to the given one. This…
A tableau calculus is proposed, based on a compressed representation of clauses, where literals sharing a similar shape may be merged. The inferences applied on these literals are fused when possible, which reduces the size of the proof. It…