相关论文: Deciding Quantifier-Free Presburger Formulas Using…
Parametric linear systems are linear systems of equations in which some symbolic parameters, that is, symbols that are not considered to be candidates for elimination or solution in the course of analyzing the problem, appear in the…
The problem of variable-rate lossless data compression is considered, for codes with and without prefix constraints. Sharp bounds are derived for the best achievable compression rate of memoryless sources, when the excess-rate probability…
In this paper, we study binary constrained codes that are resilient to bit-flip errors and erasures. In our first approach, we compute the sizes of constrained subcodes of linear codes. Since there exist well-known linear codes that achieve…
Two contrasting algorithmic paradigms for constraint satisfaction problems are successive local explorations of neighboring configurations versus producing new configurations using global information about the problem (e.g. approximating…
In this paper we derive new upper bounds for the densities of measurable sets in R^n which avoid a finite set of prescribed distances. The new bounds come from the solution of a linear programming problem. We apply this method to obtain new…
In probabilistic program analysis, quantitative analysis aims at deriving tight numerical bounds for probabilistic properties such as expectation and assertion probability. Most previous works consider numerical bounds over the whole…
This paper introduces a generic framework that provides sufficient conditions for guaranteeing polynomial-time decidability of fixed-negation fragments of first-order theories that adhere to certain fixed-parameter tractability…
We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is…
We consider an extended model of quantum computation where a scalable fault-tolerant quantum computer is coupled to one or more ancilla qubits that evolve according to a nonlinear Schr\"odinger equation. Following the approach of Abrams and…
We consider Presburger arithmetic (PA) extended by scalar multiplication by an algebraic irrational number $\alpha$, and call this extension $\alpha$-Presburger arithmetic ($\alpha$-PA). We show that the complexity of deciding sentences in…
Deciding feasibility of large systems of linear equations and inequalities is one of the most fundamental algorithmic tasks. However, due to data inaccuracies or modeling errors, in practical applications one often faces linear systems that…
This paper analyzes to what extent it is possible to efficiently reduce the number of clauses in NP-hard satisfiability problems, without changing the answer. Upper and lower bounds are established using the concept of kernelization.…
We investigate expansions of Presburger arithmetic, i.e., the theory of the integers with addition and order, with additional structure related to exponentiation: either a function that takes a number to the power of $2$, or a predicate for…
Classical PAC generalization bounds on the prediction risk of a classifier are insufficient to provide theoretical guarantees on fairness when the goal is to learn models balancing predictive risk and fairness constraints. We propose a…
Computer programs, so-called solvers, for solving the well-known Boolean satisfiability problem (Sat) have been improving for decades. Among the reasons, why these solvers are so fast, is the implicit usage of the formula's structural…
Weight quantisation is an essential technique for enabling efficient training and deployment of modern deep learning models. However, the recipe book of quantisation formats is large and formats are often chosen empirically. In this paper,…
This paper argues that the method of least squares has significant unfulfilled potential in modern machine learning, far beyond merely being a tool for fitting linear models. To release its potential, we derive custom gradients that…
Typestate systems ensure many desirable properties of imperative programs, including initialization of object fields and correct use of stateful library interfaces. Abstract sets with cardinality constraints naturally generalize typestate…
In this paper, we propose an abstract procedure for debiasing constrained or regularized potentially high-dimensional linear models. It is elementary to show that the proposed procedure can produce $\frac{1}{\sqrt{n}}$-confidence intervals…
The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…