Related papers: Caterpillar dualities and regular languages
Strong external difference families (SEDFs) are much-studied combinatorial objects motivated by an information security application. A well-known conjecture states that only one abelian SEDF with more than 2 sets exists. We show that if the…
We treat here the interrelation between formal languages and those dynamical systems that can be described by cellular automata (CA). There is a well-known injective map which identifies any CA-invariant subshift with a central formal…
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…
For a primal-dual pair of conic linear problems that are described by convex cones $S\subset X$, $T\subset Y$, bilinear symmetric objective functions $\langle\cdot,\cdot\rangle_X$, $\langle\cdot,\cdot\rangle_Y$ and a linear operator…
Human beings possess the most sophisticated computational machinery in the known universe. We can understand language of rich descriptive power, and communicate in the same environment with astonishing clarity. Two of the many contributors…
We study parameterized Constraint Satisfaction Problem for infinite constraint languages. The parameters that we study are weight of the satisfying assignment, number of constraints, maximum number of occurrences of a variable in the…
Regular synchronization languages can be used to define rational relations of finite words, and to characterize subclasses of rational relations, like automatic or recognizable relations. We provide a systematic study of the decidability of…
We investigate regular realizability (RR) problems, which are the problems of verifying whether intersection of a regular language -- the input of the problem -- and fixed language called filter is non-empty. We consider two kind of…
Tiling recognizable two-dimensional languages, also known as REC, generalize recognizable string languages to two dimensions and share with them several theoretical properties. Nevertheless REC is not closed under complementation and the…
Ambiguity is ubiquitous in natural language. Resolving ambiguous meanings is especially important in information retrieval tasks. While word embeddings carry semantic information, they fail to handle ambiguity well. Transformer models have…
We study consistent query answering in relational databases. We consider an expressive class of schema constraints that generalizes both tuple-generating dependencies and equality-generating dependencies. We establish the complexity of…
Constraint answer set programming is a promising research direction that integrates answer set programming with constraint processing. It is often informally related to the field of satisfiability modulo theories. Yet, the exact formal link…
Congruence families, i.e., $\ell$-adic convergence for well-defined arithmetic subsequences, is a commonplace phenomenon for the coefficients of modular forms. Such families superficially resemble one another, but they often vary…
In semidefinite programming (SDP), unlike in linear programming, Farkas' lemma may fail to prove infeasibility. Here we obtain an exact, short certificate of infeasibility in SDP by an elementary approach: we reformulate any semidefinite…
The closure of a discrete exponential family is described by a finite set of equations corresponding to the circuits of an underlying oriented matroid. These equations are similar to the equations used in algebraic statistics, although they…
We relate duality mappings to the "Babbage equation" F(F(z)) = z, with F a map linking weak- to strong-coupling theories. Under fairly general conditions F may only be a specific conformal transformation of the fractional linear type. This…
We study learning of indexed families from positive data where a learner can freely choose a hypothesis space (with uniformly decidable membership) comprising at least the languages to be learned. This abstracts a very universal learning…
In a recent paper it has been shown that if Cesaro and Abel limits for a certain discrete time optimal control problem are not equal, then there is a duality gap between a certain infinite-dimensional linear programming problem and its…
Some relations between families of two-character CFTs are explained using a slightly generalised coset construction, and the underlying theories (whose existence was only conjectured based on the modular differential equation) are…
The main goal of this paper is to investigate strong duality of non-convex semidefinite programming problems (SDPs). In the optimization community, it is well-known that a convex optimization problem satisfies strong duality if the Slater's…