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Matrix Graph Grammars (MGG) is a novel approach to the study of graph dynamics ([15]). In the present contribution we look at MGG as a formal grammar and as a model of computation, which is a necessary step in the more ambitious program of…
We propose a novel method for automatic program synthesis. P-Tree Programming represents the program search space through a single probabilistic prototype tree. From this prototype tree we form program instances which we evaluate on a given…
We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…
As data are increasingly modeled as graphs for expressing complex relationships, the tree pattern query on graph-structured data becomes an important type of queries in real-world applications. Most practical query languages, such as XQuery…
Predicate intuitionistic logic is a well established fragment of dependent types. According to the Curry-Howard isomorphism proof construction in the logic corresponds well to synthesis of a program the type of which is a given formula. We…
Proof autoformalization, the task of translating natural language theorems and proofs into machine-verifiable code, is a critical step for integrating large language models into rigorous mathematical workflows. Current approaches focus on…
A theory graph is a network of axiomatic theories connected with meaning-preserving mappings called theory morphisms. Theory graphs are well suited for organizing large bodies of mathematical knowledge. Traditional and formal proofs do not…
Retrieval-augmented generation (RAG) enhances large language models with external knowledge, and tree-based RAG organizes documents into hierarchical indexes to support queries at multiple granularities. However, existing Tree-RAG methods…
General treebank analyses are graph structured, but parsers are typically restricted to tree structures for efficiency and modeling reasons. We propose a new representation and algorithm for a class of graph structures that is flexible…
Applications of graph transformation (GT) systems often require control structures that can be used to direct GT processes. Most existing GT tools follow a stateful computational model, where a single graph is repeatedly modified "in-place"…
In this paper, we present structural abstraction refinement, a novel framework for verifying the threshold problem of probabilistic programs. Our approach represents the structure of a Probabilistic Control-Flow Automaton (PCFA) as a Markov…
Recent advancements in large-scale models, such as GPT-4, have showcased remarkable capabilities in addressing standard queries. However, when facing complex problems that require multi-step logical reasoning, their accuracy dramatically…
Satisfiability of boolean formulae (SAT) has been a topic of research in logic and computer science for a long time. In this paper we are interested in understanding the structure of satisfiable and unsatisfiable sentences. In previous work…
Automatic (i.e., computer-assisted) theorem proving (ATP) can come in many flavors. This document presents early steps in our effort towards defining object-oriented theorem proving (OOTP) as a new style of ATP. Traditional theorem proving…
We first propose algorithms for checking language equivalence of finite automata over a large alphabet. We use symbolic automata, where the transition function is compactly represented using a (multi-terminal) binary decision diagrams…
I propose a system for Automated Theorem Proving in higher order logic using deep learning and eschewing hand-constructed features. Holophrasm exploits the formalism of the Metamath language and explores partial proof trees using a…
We provide new insights on the determinization and minimization of tree automata using congruences on trees. From this perspective, we study a Brzozowski's style minimization algorithm for tree automata. First, we prove correct this method…
Originally proposed for handling time series data, Auto-regressive Decision Trees (ARDTs) have not yet been explored for language modeling. This paper delves into both the theoretical and practical applications of ARDTs in this new context.…
The role of uncertainty in data management has become more prominent than ever before, especially because of the growing importance of machine learning-driven applications that produce large uncertain databases. A well-known approach to…
Real-world Table-Text question answering (QA) tasks require models that can reason across long text and source tables, traversing multiple hops and executing complex operations such as aggregation. Yet existing benchmarks are small,…