Related papers: 312-Avoiding Reduced Valid Hook Configurations and…
Let $\R$ be a real closed field, $\mathcal{P},\mathcal{Q} \subset \R[X_1,...,X_k]$ finite subsets of polynomials, with the degrees of the polynomials in $\mathcal{P}$ (resp. $\mathcal{Q}$) bounded by $d$ (resp. $d_0$). Let $V \subset \R^k$…
We study the fundamental issue of decidability of satisfiability over string logics with concatenations and finite-state transducers as atomic operations. Although restricting to one type of operations yields decidability, little is known…
The observed frequency of the longest proper prefix, the longest proper suffix, and the longest infix of a word $w$ in a given sequence $x$ can be used for classifying $w$ as avoided or overabundant. The definitions used for the expectation…
The set of permutations on a finite set can be given the lattice structure known as the weak Bruhat order. This lattice structure is generalized to the set of words on a fixed alphabet $\Sigma$ = {x,y,z,...}, where each letter has a fixed…
Large language models demonstrate promising long context processing capabilities, with recent models touting context windows close to one million tokens. However, the evaluations supporting these claims often involve simple retrieval tasks…
Pudl\'ak [Pud17] lists several major conjectures from the field of proof complexity and asks for oracles that separate corresponding relativized conjectures. Among these conjectures are: - $\mathsf{DisjNP}$: The class of all disjoint…
In combinatorics on words, a word $w$ over an alphabet $\Sigma$ is said to avoid a pattern $p$ over an alphabet $\Delta$ if there is no factor $f$ of $w$ such that $f= (p)$ where $h: \Delta^*\to\Sigma^*$ is a non-erasing morphism. A pattern…
Conflict-avoiding codes are used in the multiple-access collision channel without feedback. The number of codewords in a conflict-avoiding code is the number of potential users that can be supported in the system. In this paper, a new upper…
A permutation $\pi$ contains a pattern $\sigma$ if and only if there is a subsequence in $\pi$ with its letters are in the same relative order as those in $\sigma$. Partially ordered patterns (POPs) provide a convenient way to denote…
Dependency distance minimization (DDm) is a well-established principle of word order. It has been predicted theoretically that DDm implies compression, namely the minimization of word lengths. This is a second order prediction because it…
Tandem duplication is an evolutionary process whereby a segment of DNA is replicated and proximally inserted. The different configurations that can arise from this process give rise to some interesting combinatorial questions. Firstly, we…
In this paper we prove that among the permutations of length n with i fixed points and j excedances, the number of 321-avoiding ones equals the number of 132-avoiding ones, for all given i,j<=n. We use a new technique involving diagonals of…
We study the problem of predicting a set or list of options under knapsack constraint. The quality of such lists are evaluated by a submodular reward function that measures both quality and diversity. Similar to DAgger (Ross et al., 2010),…
Motivated by modern applications, such as online advertisement and recommender systems, we study the top-$k$ extreme contextual bandits problem, where the total number of arms can be enormous, and the learner is allowed to select $k$ arms…
When many labels are possible, choosing a single one can lead to low precision. A common alternative, referred to as top-$K$ classification, is to choose some number $K$ (commonly around 5) and to return the $K$ labels with the highest…
We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…
We consider the HRT conjecture in the mixed-integer setting, where a finite configuration in $\R^d\times\R^d$ consists of $N-1$ points in $\Z^d\times\Z^d$ and one point $(\alpha,\beta)$ outside the lattice. Assuming a linear dependence…
Constrained Horn Clauses (CHCs) are an intermediate program representation that can be generated by several verification tools, and that can be processed and solved by a number of Horn solvers. One of the main challenges when using CHCs in…
Word embedding is a powerful tool in natural language processing. In this paper we consider the problem of word embedding composition \--- given vector representations of two words, compute a vector for the entire phrase. We give a…
In probabilistic logic entailments, even moderate size problems can yield linear constraint systems with so many variables that exact methods are impractical. This difficulty can be remedied in many cases of interest by introducing a three…