Related papers: Higher-Order Nonemptiness Step by Step
An automaton is unambiguous if for every input it has at most one accepting computation. An automaton is k-ambiguous (for k > 0) if for every input it has at most k accepting computations. An automaton is boundedly ambiguous if it is…
The power of natural language generation models has provoked a flurry of interest in automatic methods to detect if a piece of text is human or machine-authored. The problem so far has been framed in a standard supervised way and consists…
We study the rank one completion problem for tensors of arbitrary orders. The notion of rank one determinable tensors is introduced. We explore its properties and propose a recursive algorithm for computing rank one tensor completion. This…
We provide improved convergence rates for various \emph{non-smooth} optimization problems via higher-order accelerated methods. In the case of $\ell_\infty$ regression, we achieves an $O(\epsilon^{-4/5})$ iteration complexity, breaking the…
A reliable technique for deductive program verification should be proven sound with respect to the semantics of the programming language. For each different language, the construction of a separate soundness proof is often a laborious…
Large language models possess impressive capabilities in generating programs (e.g., Python) from natural language descriptions to execute robotic tasks. However, these generated programs often contain errors that violate externally given…
We study the problem of generating, ranking and unranking of unlabeled ordered trees whose nodes have maximum degree of $\Delta$. This class of trees represents a generalization of chemical trees. A chemical tree is an unlabeled tree in…
Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length $n$ and fixed order $r.$ An algorithm is designed that has complexity of order $n\log n$ and corrects most error patterns of weight up to…
Explanation-based generalization is used to extract a specialized grammar from the original one using a training corpus of parse trees. This allows very much faster parsing and gives a lower error rate, at the price of a small loss in…
Large Language Models (LLMs) such as GPT-4 have demonstrated their ability to understand natural language and generate complex code snippets. This paper introduces a novel Large Language Model Evolutionary Algorithm (LLaMEA) framework,…
Enumeration algorithms have been one of recent hot topics in theoretical computer science. Different from other problems, enumeration has many interesting aspects, such as the computation time can be shorter than the total output size, by…
Motivated by the study of pattern avoidance in the context of permutations and ordered partitions, we consider the enumeration of weak-ordering chains obtained as leaves of certain restricted rooted trees. A tree of order $n$ is generated…
We describe a method for proving non-looping non-termination, that is, of term rewriting systems that do not admit looping reductions. As certificates of non-termination, we employ regular (tree) automata.
In machine learning ensemble methods have demonstrated high accuracy for the variety of problems in different areas. Two notable ensemble methods widely used in practice are gradient boosting and random forests. In this paper we present…
We consider algorithms and lower bounds for various problems over forest languages; as input models we allow forest algebras, deterministic forest automata and nondeterministic forest automata. For the equivalence problem, we give an…
We show that a recently discovered fourth order symplectic algorithm, which requires one evaluation of force gradient in addition to three evaluations of the force, when iterated to higher order, yielded algorithms that are far superior to…
Algorithms for model checking and satisfiability of the modal $\mu$-calculus start by converting formulas to alternating parity tree automata. Thus, model checking is reduced to checking acceptance by tree automata and satisfiability to…
Treebanks, such as the Penn Treebank (PTB), offer a simple approach to obtaining a broad coverage grammar: one can simply read the grammar off the parse trees in the treebank. While such a grammar is easy to obtain, a square-root rate of…
We present an algorithm that, on input $n$, lists every unlabeled tree of order $n$.
We consider, as a means of making programming languages more flexible and powerful, a parsing algorithm in which the parser may freely modify the grammar while parsing. We are particularly interested in a modification of the canonical LR(1)…