相关论文: Simple minimally unsatisfiable subsets of 2-CNFs
Modular invariance strongly constrains the spectrum of states of two dimensional conformal field theories. By summing over the images of the modular group, we construct candidate CFT partition functions that are modular invariant and have…
The main result of this paper is the decidability of the membership problem for $2\times 2$ nonsingular integer matrices. Namely, we will construct the first algorithm that for any nonsingular $2\times 2$ integer matrices $M_1,\dots,M_n$…
Rule sets are highly interpretable logical models in which the predicates for decision are expressed in disjunctive normal form (DNF, OR-of-ANDs), or, equivalently, the overall model comprises an unordered collection of if-then decision…
We study the problem of approximating and learning coverage functions. A function $c: 2^{[n]} \rightarrow \mathbf{R}^{+}$ is a coverage function, if there exists a universe $U$ with non-negative weights $w(u)$ for each $u \in U$ and subsets…
Boolean satisfiability ({\SAT}) has played a key role in diverse areas spanning testing, formal verification, planning, optimization, inferencing and the like. Apart from the classical problem of checking boolean satisfiability, the…
We study the Constraint Satisfaction Problem CSP(A), where A is first-order definable in (Z;+,1) and contains +. We prove such problems are either in P or NP-complete.
Satisfiability checking for monotone modal logic is known to be (only) NP-complete. We show that this remains true when the logic is extended with aconjunctive and alternation-free fixpoint operators as well as the universal modality; the…
This paper presents a method for solving the supervised learning problem in which the output is highly nonlinear and discontinuous. It is proposed to solve this problem in three stages: (i) cluster the pairs of input-output data points,…
Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…
We consider the problem EnumIP of enumerating prime implicants of Boolean functions represented by decision decomposable negation normal form (dec-DNNF) circuits. We study EnumIP from dec-DNNF within the framework of enumeration complexity…
A novel parallel algorithm for solving the classical Decision Boolean Satisfiability problem with clauses in conjunctive normal form is depicted. My approach for solving SAT is without using algebra or other computational search strategies…
We define and solve classes of sparse matrix problems that arise in multilevel modeling and data analysis. The classes are indexed by the number of nested units, with two-level problems corresponding to the common situation in which data on…
We demonstrate the usefulness of submodularity in statistics as a characterization of the difficulty of the \emph{search} problem of feature selection. The search problem is the ability of a procedure to identify an informative set of…
Modular invariance imposes rigid constrains on the partition functions of two-dimensional conformal field theories. Many fundamental results follow strictly from modular invariance, giving rise to the numerical modular bootstrap program.…
Motivated by applications in redistricting, we consider the uniform capacitated k-median and uniform capacitated k-means problems in bounded doubling metrics. We provide the first QPTAS for both problems and the first PTAS for the uniform…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
The estimation of phase transitions in random boolean Constraint Satisfaction Problems (CSP) is based on two fundamental tools: the first and second moment methods. While the first moment method on the number of solutions permits to compute…
This paper studies the completeness of conjunctive queries over a partially complete database and the approximation of incomplete queries. Given a query and a set of completeness rules (a special kind of tuple generating dependencies) that…
Medical multimodal representation learning aims to integrate heterogeneous clinical data into unified patient representations to support predictive modeling, which remains an essential yet challenging task in the medical data mining…
We show existence and uniqueness for timelike minimal submanifolds in ambient Lorentz manifolds admitting a time function. The initial value formulation introduced and the conditions imposed on the initial data are given in purely geometric…