相关论文: Solving the Weighted HOM-Problem With the Help of …

In this paper, we study three algorithmic problems involving computation trees: the optimization, solvability, and satisfiability problems. The solvability problem is concerned with recognizing computation trees that solve problems. The…

We prove decidability of the boundedness problem for monadic least fixed-point recursion based on positive monadic second-order (MSO) formulae over trees. Given an MSO-formula phi(X,x) that is positive in X, it is decidable whether the…

Homographs, words with the same spelling but different meanings, remain challenging in Neural Machine Translation (NMT). While recent works leverage various word embedding approaches to differentiate word sense in NMT, they do not focus on…

We introduce regular graph constraints and explore their decidability properties. The motivation for regular graph constraints is 1) type checking of changing types of objects in the presence of linked data structures, 2) shape analysis…

There are many types of automata and grammar models that have been studied in the literature, and for these models, it is common to determine whether certain problems are decidable. One problem that has been difficult to answer throughout…

Many fundamental problems in extremal combinatorics are equivalent to proving certain polynomial inequalities in graph homomorphism densities. In 2011, a breakthrough result by Hatami and Norine showed that it is undecidable to verify…

The Hom complex $\mathrm{Hom}(G, H)$ of graphs is a simplicial complex associated to a pair of graphs $G$ and $H$, and its homotopy type is of interest in the graph coloring problem and the homomorphism reconfiguration problem. In this…

For every fixed graph $H$, it is known that homomorphism counts from $H$ and colorful $H$-subgraph counts can be determined in $O(n^{t+1})$ time on $n$-vertex input graphs $G$, where $t$ is the treewidth of $H$. On the other hand, a running…

A practical automatic textual math word problems (MWPs) solver should be able to solve various textual MWPs while most existing works only focused on one-unknown linear MWPs. Herein, we propose a simple but efficient method called Universal…

Many important graph theoretic notions can be encoded as counting graph homomorphism problems, such as partition functions in statistical physics, in particular, independent sets and colourings. In this article we study the complexity of…

We study the portraits of isometries of rooted trees - the labelling of the tree, at each vertex, by the permutation of its descendants - in terms of languages. We characterize regularly branched self-similar groups in terms of…

Machine learning in high-stakes domains, such as healthcare, faces two critical challenges: (1) generalizing to diverse data distributions given limited training data while (2) maintaining interpretability. To address these challenges, we…

Subzero automata is a class of tree automata whose acceptance condition can express probabilistic constraints. Our main result is that the problem of determining if a subzero automaton accepts some regular tree is decidable.

We define a class of ranked tree automata TABG generalizing both the tree automata with local tests between brothers of Bogaert and Tison (1992) and with global equality and disequality constraints (TAGED) of Filiot et al. (2007). TABG can…

The homomorphism problem for relational structures is an abstract way of formulating constraint satisfaction problems (CSP) and various problems in database theory. The decision version of the homomorphism problem received a lot of…

In the 1990s, Steel and Woodin showed that under large cardinal hypotheses, the HOD of $L(\mathbb R)$ admits a fine-structural analysis. Although this theorem sheds light on various problems in descriptive set theory, the fine-structural…

For a given regular language of infinite trees, one can ask about the minimal number of priorities needed to recognize this language with a non-deterministic, alternating, or weak alternating parity automaton. These questions are known as,…

We show that the following problems are decidable in a rank 2 free group F_2: does a given finitely generated subgroup H contain primitive elements? and does H meet the orbit of a given word u under the action of G, the group of…

Higher-order unification has been shown to be undecidable. Miller discovered the pattern fragment and subsequently showed that higher-order pattern unification is decidable and has most general unifiers. We extend the algorithm to…

Topic models uncover latent thematic structures in text corpora, yet evaluating their quality remains challenging, particularly in specialized domains. Existing methods often rely on automated metrics like topic coherence and diversity,…