相关论文: A Tractable Extension of Linear Indexed Grammars

Lexical semantics theories differ in advocating that the meaning of words is represented as an inference graph, a feature mapping or a vector space, thus raising the question: is it the case that one of these approaches is superior to the…

We combine dependent types with linear type systems that soundly and completely capture polynomial time computation. We explore two systems for capturing polynomial time: one system that disallows construction of iterable data, and one,…

Advancing the frontier of subquadratic architectures for Language Models (LMs) is crucial in the rapidly evolving field of natural language processing. Current innovations, including State Space Models, were initially celebrated for…

We show that any multiple-valued function can be represented by a linear lambda term typed in a second-order polymorphic type system, using two distinct styles. The first is a circuit style, which mimics combinational circuits in switching…

This paper is an extended abstract of an analysis of term rewriting where the terms in the rewrite rules as well as the term to be rewritten are compressed by a singleton tree grammar (STG). This form of compression is more general than…

We address the issue of how to associate frequency information with lexicalized grammar formalisms, using Lexicalized Tree Adjoining Grammar as a representative framework. We consider systematically a number of alternative probabilistic…

We introduce LAM, a subsystem of IMALL2 with restricted additive rules able to manage duplication linearly, called linear additive rules. LAM is presented as the type assignment system for a calculus endowed with copy constructors, which…

We continue to investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation. In an earlier article we had introduced the distinction between periodic and…

The functional approach to compositional distributional semantics considers transitive verbs to be linear maps that transform the distributional vectors representing nouns into a vector representing a sentence. We conduct an initial…

We present a system for the investigation of computational properties of categorial grammar parsing based on a labelled analytic tableaux theorem prover. This proof method allows us to take a modular approach, in which the basic grammar can…

The heterogeneity of tools that support temporal logic formulae poses several challenges in terms of interoperability. In particular, a standard syntax for temporal logic on finite traces, despite similar to the one for infinite traces, is…

In a previous work we introduced Dual Light Affine Logic (DLAL) ([BaillotTerui04]) as a variant of Light Linear Logic suitable for guaranteeing complexity properties on lambda-calculus terms: all typable terms can be evaluated in polynomial…

Let G be a connected compact Lie group acting on a manifold M and let D be a transversally elliptic operator on M. The multiplicity of the index of D is a function on the set of irreducible representations of G. Let T be a maximal torus of…

In functional programming languages, generalized algebraic data types (GADTs) are very useful as the unnecessary pattern matching over them can be ruled out by the failure of unification of type arguments. In dependent type systems, this is…

We introduce a novel resource analysis for typed term rewrite systems based on a potential-based type system. This type system gives rise to polynomial bounds on the innermost runtime complexity. We relate the thus obtained amortised…

We study the polyregular string-to-string functions, which are certain functions of polynomial output size that can be described using automata and logic. We describe a system of combinators that generates exactly these functions. Unlike…

In formal argumentation, a distinction can be made between extension-based semantics, where sets of arguments are either (jointly) accepted or not, and ranking-based semantics, where grades of acceptability are assigned to arguments.…

This is the first installment of an exposition of an ACL2 formalization of elementary linear algebra, focusing on aspects of the subject that apply to matrices over an arbitrary commutative ring with identity, in anticipation of a future…

This paper introduces the idea of applying signal processing inside a Large Language Model (LLM). With the recent explosion of generative AI, our work can help bridge two fields together, namely the field of signal processing and large…

In this paper we show that an account for coordination can be constructed using the derivation structures in a lexicalized Tree Adjoining Grammar (LTAG). We present a notion of derivation in LTAGs that preserves the notion of fixed…