Related papers: On the CNF encoding of cardinality constraints and…
Pseudo-Boolean constraints are omnipresent in practical applications, and thus a significant effort has been devoted to the development of good SAT encoding techniques for them. Some of these encodings first construct a Binary Decision…
In this paper we study the fine-grained complexity of the CFL reachability problem. We first present one of the existing algorithms for the problem and an overview of conditional lower bounds based on widely believed hypotheses. We then use…
Nowadays there are several classes of constrained codes intended for different applications. The following two large classes can be distinguished. The first class contains codes with local constraints; for example, the source data must be…
Many binary classification problems minimize misclassification above (or below) a threshold. We show that instances of ranking problems, accuracy at the top or hypothesis testing may be written in this form. We propose a general framework…
This paper explores the integration of Diophantine equations into neural network (NN) architectures to improve model interpretability, stability, and efficiency. By encoding and decoding neural network parameters as integer solutions to…
New measures for the quantization of systems with constraints are discussed and applied to several examples, in particular, examples of alternative but equivalent formulations of given first-class constraints, as well as a comparison of…
We propose a novel way to incorporate expert knowledge into the training of deep neural networks. Many approaches encode domain constraints directly into the network architecture, requiring non-trivial or domain-specific engineering. In…
We present a novel framework for embedding hard constraint satisfaction into neural network (NN) architectures, specifically feedforward neural networks and transformers, with input-dependent affine constraints of arbitrary cardinality.…
This paper investigates the problem of decomposition with respect to outputs for Boolean control networks (BCNs). First, with the linear expression of BCNs and the matrix semi-tensor product, some algebraic equivalent conditions for the…
Formal reasoning about finite sets and cardinality is an important tool for many applications, including software verification, where very often one needs to reason about the size of a given data structure and not only about what its…
One of the few available complete methods for checking the satisfiability of sets of polynomial constraints over the reals is the cylindrical algebraic covering (CAlC) method. In this paper, we propose an extension for this method to…
Several techniques and tools have been developed for verification of properties expressed as Horn clauses with constraints over a background theory (CHC). Current CHC verification tools implement intricate algorithms and are often limited…
We introduce statistical constraints, a declarative modelling tool that links statistics and constraint programming. We discuss two statistical constraints and some associated filtering algorithms. Finally, we illustrate applications to…
We present an experimental study of the effects of quantifier alternations on the evaluation of quantified Boolean formula (QBF) solvers. The number of quantifier alternations in a QBF in prenex conjunctive normal form (PCNF) is directly…
This short note introduces a novel diagnostic tool for evaluating the convection boundedness properties of numerical schemes across discontinuities. The proposed method is based on the convection boundedness criterion and the normalised…
We study Boolean circuits as a representation of Boolean functions and consider different equivalence, audit, and enumeration problems. For a number of restricted sets of gate types (bases) we obtain efficient algorithms, while for all…
Causal discovery studies the problem of mining causal relationships between variables from data, which is of primary interest in science. During the past decades, significant amount of progresses have been made toward this fundamental data…
In this paper, we propose a novel Control Barrier Function (CBF) based controller for nonlinear systems with complex, time-varying input constraints. To deal with these constraints, we introduce an auxiliary control input to transform the…
The fractional Calder\'on problem asks to determine the unknown coefficients in a nonlocal, elliptic equation of fractional order from exterior measurements of its solutions. There has been substantial work on many aspects of this inverse…
Decoding of convolutional codes poses a significant challenge for coding theory. Classical methods, based on e.g. Viterbi decoding, suffer from being computationally expensive and are restricted therefore to codes of small complexity. Based…