Related papers: Superredundancy: A tool for Boolean formula minimi…
The seminal work of Bencz\'ur and Karger demonstrated cut sparsifiers of near-linear size. Subsequent extensions have yielded sparsifiers for hypergraph cuts and more recently linear codes over Abelian groups. A decade ago, Kogan and…
Dependently typed lambda calculi such as the Logical Framework (LF) are capable of representing relationships between terms through types. By exploiting the "formulas-as-types" notion, such calculi can also encode the correspondence between…
Counting distinct permutations with replacement, especially when involving multiple subwords, is a longstanding challenge in combinatorial analysis, with critical applications in cryptography, bioinformatics, and statistical modeling. This…
The complete reason behind a decision is a Boolean formula that characterizes why the decision was made. This recently introduced notion has a number of applications, which include generating explanations, detecting decision bias and…
A supercongruence is a congruence between rational numbers modulo a power of a prime. In this paper, we give a technique for finding and algorithmically proving supercongruences by expressing terms as infinite series involving certain…
The backbone of a Boolean formula is the set of literals that must be true in every assignment that satisfies the formula. This concept is fundamental to key operations on variability models, including propagating user configuration…
We establish a new bridge between propositional logic and elementary number theory. The main objects are "minimally unsatisfiable clause-sets", short "MUs", unsatisfiable conjunctive normal forms rendered satisfiable by elimination of any…
We consider the complexities of substitutive sequences over a binary alphabet. By studying various types of special words, we show that, knowing some initial values, its complexity can be completely formulated via a recurrence formula…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
This paper tackles the reduction of redundant repeating generation that is often observed in RNN-based encoder-decoder models. Our basic idea is to jointly estimate the upper-bound frequency of each target vocabulary in the encoder and…
Large Reasoning Models (LRMs) often suffer from overthinking, generating verbose reasoning traces that compromise both computational efficiency and interpretability. Unlike prior efforts that rely on global length-based rewards, we propose…
Learning pseudo-Boolean (PB) constraints in PB solvers exploiting cutting planes based inference is not as well understood as clause learning in conflict-driven clause learning solvers. In this paper, we show that PB constraints derived…
Reverse Mathematics (RM for short) is a program in the foundations of mathematics with the aim of finding the minimal axioms required for proving theorems about countable and separable objects. RM usually takes place in second-order…
Properties of Term Rewriting Systems are called modular iff they are preserved under (and reflected by) disjoint union, i.e. when combining two Term Rewriting Systems with disjoint signatures. Convergence is the property of Infinitary Term…
Traditionally it had been a problem that researchers did not have access to enough spatial data to answer pressing research questions or build compelling visualizations. Today, however, the problem is often that we have too much data.…
The reduction of constraints to obtain minimal representations of sets is a very common problem in many engineering applications. While well-established methodologies exist for the case of linear constraints, the problem of how to detect…
We introduce new definitions of universal and superuniversal computable codes, which are based on a code's ability to approximate Kolmogorov complexity within the prescribed margin for all individual sequences from a given set. Such sets of…
This paper mainly studies nonnegativity decision of forms based on variable substitutions. Unlike existing research, the paper regards simplex subdivisions as new perspectives to study variable substitutions, gives some subdivisions of the…
The objective of this paper is to improve the customary definition of redundancy by providing quantitative measures in its place, which we coin upper and lower redundancies, that match better with an intuitive understanding of redundancy…
Redundancy of experimental data is the basic statistic from which the complexity of a natural phenomenon and the proper number of experiments needed for its exploration can be estimated. The redundancy is expressed by the entropy of…