Related papers: Introducing Proof Tree Automata and Proof Tree Gra…
ProbLog is a popular probabilistic logic programming language/tool, widely used for applications requiring to deal with inherent uncertainties in structured domains. In this paper we study connections between ProbLog and a variant of…
The advent of language implementation tools such as PyPy and Truffle/Graal have reinvigorated and broadened interest in topics related to automatic compiler generation and optimization. Given this broader interest, we revisit the Futamura…
So far, a very large amount of work in Natural Language Processing (NLP) rely on trees as the core mathematical structure to represent linguistic informations (e.g. in Chomsky's work). However, some linguistic phenomena do not cope properly…
We introduce Tinker, a tool for designing and evaluating proof strategies based on proof-strategy graphs, a formalism previously introduced by the authors. We represent proof strategies as open-graphs, which are directed graphs with…
Graph reasoning agents operating from natural-language inputs must solve a coupled problem: they must reconstruct a structured graph instance from text, decide whether existing computational assets are sufficient, interact with tools under…
We study trees where each successor set is equipped with some additional structure. We introduce a family of automaton models for such trees and prove their equivalence to certain fixed-point logics. As a consequence we obtain…
We give a proof for sharp estimate for the number of spanning trees using linear algebra and generalize this bound to multigraphs. In addition, we show that this bound is tight for complete graphs. In addition, we give estimates for number…
Sequent calculus is widely used for formalizing proofs. However, due to the proliferation of data, understanding the proofs of even simple mathematical arguments soon becomes impossible. Graphical user interfaces help in this matter, but…
Current Large Language Models (LLMs) exhibit limited ability to understand table structures and to apply precise numerical reasoning, which is crucial for tasks such as table question answering (TQA) and table-based fact verification (TFV).…
Walnut is a software that using automata can prove theorems in combinatorics on words about automatic sequences. We are able to apply this software to both prove new results as well as reprove some old results on avoiding squares and cubes…
The knowledge graph is a structure to store and represent knowledge, and recent studies have discussed its capability to assist language models for various applications. Some variations of knowledge graphs aim to record arguments and their…
In the recent years, we have linked a large corpus of formal mathematics with automated theorem proving (ATP) tools, and started to develop combined AI/ATP systems working in this setting. In this paper we first relate this project to the…
Structural measures of graphs, such as treewidth, are central tools in computational complexity resulting in efficient algorithms when exploiting the parameter. It is even known that modern SAT solvers work efficiently on instances of small…
A novel graph-to-tree conversion mechanism called the deep-tree generation (DTG) algorithm is first proposed to predict text data represented by graphs. The DTG method can generate a richer and more accurate representation for nodes (or…
We outline a program in the area of formalization of mathematics to automate theorem proving in algebra and algebraic geometry. We propose a construction of a dictionary between automated theorem provers and (La)TeX exploiting syntactic…
Knowledge Graphs are repositories of information that gather data from a multitude of domains and sources in the form of semantic triples, serving as a source of structured data for various crucial applications in the modern web landscape,…
Automata admitting at most one accepting run per structure, known as unambiguous automata, find applications in verification of reactive systems as they extend the class of deterministic automata whilst maintaining some of their desirable…
Text-to-Audio (TTA) aims to generate audio that corresponds to the given text description, playing a crucial role in media production. The text descriptions in TTA datasets lack rich variations and diversity, resulting in a drop in TTA…
Probabilistic timed automata (PTAs) are timed automata (TAs) extended with discrete probability distributions.They serve as a mathematical model for a wide range of applications that involve both stochastic and timed behaviours. In this…
One of the major open problems in automata and logic is the following: is there an algorithm which inputs a regular tree language and decides if the language can be defined in first-order logic? The goal of this paper is to present this…