Related papers: Symbolic Algorithms for Language Equivalence and K…
Large language models (LLMs) are often equipped with multi-sample decoding strategies. An LLM implicitly defines an arithmetic code book, facilitating efficient and embarrassingly parallelizable \textbf{arithmetic sampling} to produce…
Autoformalization, the task of automatically translating natural language descriptions into a formal language, poses a significant challenge across various domains, especially in mathematics. Recent advancements in large language models…
We give a quantum algorithm for evaluating formulas over an extended gate set, including all two- and three-bit binary gates (e.g., NAND, 3-majority). The algorithm is optimal on read-once formulas for which each gate's inputs are balanced…
Pomsets constitute one of the most basic models of concurrency. A pomset is a generalisation of a word over an alphabet in that letters may be partially ordered. A term $t$ using the bi-Kleene operations $0,1, +, \cdot\, ,^*, \parallel,…
This paper discusses the methods that we used for our submissions to the WMT 2023 Terminology Shared Task for German-to-English (DE-EN), English-to-Czech (EN-CS), and Chinese-to-English (ZH-EN) language pairs. The task aims to advance…
Decoding methods for large language models often trade-off between diversity of outputs and parallelism of computation. Methods such as beam search and Gumbel top-k sampling can guarantee a different output for each element of the beam, but…
We study the satisfiability problem of symbolic tree automata and decompose it into the satisfiability problem of the existential first-order theory of the input characters and the existential monadic second-order theory of the indices of…
The Turing machine models an old-fashioned computer, that does not interact with the user or with other computers, and only does batch processing. Therefore, we came up with a Reactive Turing Machine that does not have these shortcomings.…
As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent…
Symbolic indefinite integration in Computer Algebra Systems such as Maple involves selecting the most effective algorithm from multiple available methods. Not all methods will succeed for a given problem, and when several do, the results,…
A number of novel programming languages and libraries have been proposed that offer simpler-to-use models of concurrency than threads. It is challenging, however, to devise execution models that successfully realise their abstractions…
Textual content around us is growing on a daily basis. Numerous articles are being written as we speak on online newspapers, blogs, or social media. Similarly, recent advances in the AI field, like language models or traditional classic AI…
In the present paper, we introduce a multi-type calculus for the logic of measurable Kleene algebras, for which we prove soundness, completeness, conservativity, cut elimination and subformula property. Our proposal imports ideas and…
NetKAT is a domain-specific programming language and logic that has been successfully used to specify and verify the behavior of packet-switched networks. This paper develops techniques for automatically learning NetKAT models of unknown…
Reactive programs are ubiquitous in modern applications, and so verification is highly desirable. We present a verification strategy for reactive programs with a large or infinite state space utilising algebraic laws for reactive relations.…
Identifying semantically equivalent sentences is important for many cross-lingual and mono-lingual NLP tasks. Current approaches to semantic equivalence take a loose, sentence-level approach to "equivalence," despite previous evidence that…
Functional programs typically interact with stateful libraries that hide state behind typed abstractions. One particularly important class of applications are data structure implementations that rely on such libraries to provide a level of…
Programming languages tend to evolve over time to use more and more concepts from theoretical computer science. Still, there is a gap between programming and pure mathematics. Not all theoretical results have realized their promising…
We show that three fixed point structures equipped with (sequential) composition, a sum operation, and a fixed point operation share the same valid equations. These are the theories of (context-free) languages, (regular) tree languages, and…
In this work we use a framework of finite-state automata constructions based on equivalences over words to provide new insights on the relation between well-known methods for computing the minimal deterministic automaton of a language.