Related papers: Unit contradiction versus unit propagation
Consider the following decision problem: for a given monotone Boolean function $f$ decide, whether $f$ is read-once. For this problem, it is essential how the input function $f$ is represented. Our contribution consists of the following two…
We introduce power term polynomial algebra, a representation language for Boolean formulae designed to bridge conjunctive normal form (CNF) and algebraic normal form (ANF). The language is motivated by the tiling mismatch between these…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
Prompted by an observation about the integral of exponential functions of the form $f(x)=\lambda e^{\alpha x}$, we investigate the possibility to exactly integrate families of functions generated from a given function by scaling or by…
We consider overdetermined problems related to the fractional capacity. In particular we study $s$-harmonic functions defined in unbounded exterior sets or in bounded annular sets, and having a level set parallel to the boundary. We first…
The trace anomaly of conformal field theories in four dimensions is characterized by '$a$' and '$c$'-functions. The scaling properties of the effective action of a CFT in the presence of boundaries is shown to be determined by $a$, $c$ and…
A unary constraint (on the Boolean domain) is a function from {0,1} to the set of real numbers. A free use of auxiliary unary constraints given besides input instances has proven to be useful in establishing a complete classification of the…
An open problem in communication complexity proposed by several authors is to prove that for every Boolean function f, the task of computing f(x AND y) has polynomially related classical and quantum bounded-error complexities. We solve a…
BEE is a compiler which facilitates solving finite domain constraints by encoding them to CNF and applying an underlying SAT solver. In BEE constraints are modeled as Boolean functions which propagate information about equalities between…
The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the…
We relate two different solutions of a Mahler equation; one solution is only defined at certain roots of unity, while the other is an analytic function inside the unit disk.
We will study some important properties of Boolean functions based on newly introduced concepts called Special Decomposition of a Set and Special Covering of a Set. These concepts enable us to study important problems concerning Boolean…
We present a CLP(FD)-based constraint solver able to deal with unbounded domains. It is based on constraint propagation, resorting to enumeration if all other methods fail. An important aspect is detecting when enumeration was complete and…
In this note we compare two measures of the complexity of a class $\mathcal F$ of Boolean functions studied in (unconditional) pseudorandomness: $\mathcal F$'s ability to distinguish between biased and uniform coins (the coin problem), and…
The problem is considered as to whether a monotone function defined on a subset P of a Euclidean space can be strictly monotonically extended to the whole space. It is proved that this is the case if and only if the function is {\em…
In many decision-making processes, one may prefer multiple solutions to a single solution, which allows us to choose an appropriate solution from the set of promising solutions that are found by algorithms. Given this, finding a set of…
We show (almost) separation between certain important classes of Boolean functions. The technique that we use is to show that the total influence of functions in one class is less than the total influence of functions in the other class. In…
A uniformization of a binary relation is a function that is contained in the relation and has the same domain as the relation. The synthesis problem asks for effective uniformization for classes of relations and functions that can be…
Monotone Boolean functions are a structurally important class of Boolean functions, but their restricted form imposes strong limitations on achievable nonlinearity. In this paper, we investigate whether evolutionary computation can evolve…
We present an approach to propagation-based SAT encoding of combinatorial problems, Boolean equi-propagation, where constraints are modeled as Boolean functions which propagate information about equalities between Boolean literals. This…