Related papers: The Compilability Thresholds of 2-CNF to OBDD
We investigate theoretical guarantees for the false-negative rate (FNR) -- the fraction of true causal edges whose orientation is not recovered, under single-variable random interventions and an $\epsilon$-interventional faithfulness…
We study the problem of estimating the size of the maximum matching in the sublinear-time setting. This problem has been extensively studied, with several known upper and lower bounds. A notable result by Behnezhad (FOCS 2021) established a…
We consider the randomized decision tree complexity of the recursive 3-majority function. We prove a lower bound of $(1/2-\delta) \cdot 2.57143^h$ for the two-sided-error randomized decision tree complexity of evaluating height $h$ formulae…
A classical question of propositional logic is one of the shortest proof of a tautology. A related fundamental problem is to determine the relative efficiency of standard proof systems, where the relative complexity is measured using the…
We give a "regularity lemma" for degree-d polynomial threshold functions (PTFs) over the Boolean cube {-1,1}^n. This result shows that every degree-d PTF can be decomposed into a constant number of subfunctions such that almost all of the…
We study O(n)-symmetric two-dimensional conformal field theories (CFTs) for a continuous range of n below two. These CFTs describe the fixed point behavior of self-avoiding loops. There is a pair of known fixed points connected by an RG…
We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…
We consider 2-dimensional random simplicial complexes $Y$ in the multi-parameter model. We establish the multi-parameter threshold for the property that every 2-dimensional simplicial complex $S$ admits a topological embedding into $Y$…
In this paper we determine the threshold for collapsibility in the probabilistic model $X_d(n,p)$ of $d$-dimensional simplicial complexes. A lower bound for this threshold $p=\frac{c_d}{n}$ was established in \cite{ALLM}. Here we show that…
We describe a polynomial-time algorithm which, given a graph $G$ with treewidth $t$, approximates the pathwidth of $G$ to within a ratio of $O(t\sqrt{\log t})$. This is the first algorithm to achieve an $f(t)$-approximation for some…
We consider a uniform spanning tree in a $\delta$-square grid approximation of a planar domain $\Omega$. For given integer $n\ge 2$, we condition the tree on the following $n$-arm event: we pick $n$ branches, emanating from $n$ points…
This paper discusses examples of integral factorial ratios of height 2 or more. It classifies (apart from finitely many examples) such factorial ratios with height 2 and norm at most 1/3, and describes a general result which exhibits more…
Let $s$ be the sum-of-digits function in base $2$, which returns the number of $\mathtt 1$s in the base-2 expansion of a nonnegative integer. For a nonnegative integer $t$, define the asymptotic density \[ c_t=\lim_{N\rightarrow \infty}…
A major open problem in proof complexity is to demonstrate that random 3-CNFs with a linear number of clauses require super-polynomial size refutations in bounded-depth Frege systems. We take the first step towards addressing this question…
A two-dimensional string is simply a two-dimensional array. We continue the study of the combinatorial properties of repetitions in such strings over the binary alphabet, namely the number of distinct tandems, distinct quartics, and runs.…
In this work we analyze basic properties of Random Apollonian Networks \cite{zhang,zhou}, a popular stochastic model which generates planar graphs with power law properties. Specifically, let $k$ be a constant and $\Delta_1 \geq \Delta_2…
We establish a lower bound of $2^n$ conditional branches for deciding the satisfiability of the conjunction of any two Boolean formulas from a set called a full representation of Boolean functions of $n$ variables - a set containing a…
A propositional logic sentence in conjunctive normal form that has clauses of length two (a 2-CNF) can be associated with a multigraph in which the vertices correspond to the variables and edges to clauses. We first show that every such…
In this paper, we analyze 2CNF formulas from the perspectives of Read-Once resolution (ROR) refutation schemes. We focus on two types of ROR refutations, viz., variable-once refutation and clause-once refutation. In the former, each…
Local convergence of bounded degree graphs was introduced by Benjamini and Schramm. This result was extended further by Lyons to bounded average degree graphs. In this paper we study the convergence of random tree sequences with given…