Related papers: Combinatory Array Logic with Sums
In this paper we show examples for applications of the Bombieri-Lang conjecture in additive combinatorics, giving bounds on the cardinality of sumsets of squares and higher powers of integers. Using similar methods we give bounds on the…
Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds…
Originally developed as a theory of consciousness, integrated information theory provides a mathematical framework to quantify the causal irreducibility of systems and subsets of units in the system. Specifically, mechanism integrated…
Hybrid logic with binders is an expressive specification language. Its satisfiability problem is undecidable in general. If frames are restricted to N or general linear orders, then satisfiability is known to be decidable, but of…
We introduce a logical foundation to reason on tree structures with constraints on the number of node occurrences. Related formalisms are limited to express occurrence constraints on particular tree regions, as for instance the children of…
For a strongly connected category $\mathcal C$ with pair-wise coproducts, we introduce a cosimplicial object, which serves as a sort of resolution for computing higher derived functors of ${\sf lim} : \mathrm{Ab}^{\mathcal C}\to…
Deciding whether a graph can be embedded in a grid using only unit-length edges is NP-complete, even when restricted to binary trees. However, it is not difficult to devise a number of graph classes for which the problem is polynomial, even…
We try to bring to light some combinatorial structure underlying formal proofs in logic. We do this through the study of the Craig Interpolation Theorem which is properly a statement about the structure of formal derivations. We show that…
We study the expressive power of the two-variable fragment of order-invariant first-order logic. This logic departs from first-order logic in two ways: first, formulas are only allowed to quantify over two variables. Second, formulas can…
Exponential sums with monomials are highly related to many interesting problems in number theory and well studied by many literatures. In this paper, we consider the exponential sums with polynomials and prove a new upper bound. As an…
We give an explicit upper bound for the number of equivalence classes of binary forms with rational integral coefficients of given degree and given discriminant, and with given splitting field. Further, we give an explicit upper bound for…
Justification theory is a unifying framework for semantics of non-monotonic logics. It is built on the notion of a justification, which intuitively is a graph that explains the truth value of certain facts in a structure. Knowledge…
In many machine learning tasks, models are trained to predict structure data such as graphs. For example, in natural language processing, it is very common to parse texts into dependency trees or abstract meaning representation (AMR)…
Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which…
Within the framework of computable infinitary continuous logic, we develop a system of hyperarithmetic numerals. These numerals are infinitary sentences in a metric language $L$ that have the same truth value in every interpretation of $L$.…
We look at characterizing which formulas are expressible in rich decidable logics such as guarded fixpoint logic, unary negation fixpoint logic, and guarded negation fixpoint logic. We consider semantic characterizations of definability, as…
We investigate the complexity consequences of adding pointer arithmetic to separation logic. Specifically, we study extensions of the points-to fragment of symbolic-heap separation logic with various forms of Presburger arithmetic…
This article presents a combinatorial result on indexed languages which was inspired by an attempt to understand the structure of groups with indexed language word problem. We show that a sufficiently long word in an indexed language can be…
We explore the possibility of extending Mardare et al. quantitative algebras to the structures which naturally emerge from Combinatory Logic and the lambda-calculus. First of all, we show that the framework is indeed applicable to those…
We solve an elementary number theory problem on sums of fractional parts, using methods from group theory. We apply our result to deduce the finiteness of certain monodromy representations.