相关论文: Bounded Underapproximations
We show that any finite monoid or semigroup presentation satisfying the small overlap condition C(4) has word problem which is a deterministic rational relation. It follows that the set of lexicographically minimal words forms a regular…
Language models are now capable of solving tasks that require dealing with long sequences consisting of hundreds of thousands of tokens. However, they often fail on tasks that require repetitive use of simple rules, even on sequences that…
The rational index of a context-free language $L$ is a function $f(n)$, such that for each regular language $R$ recognized by an automaton with $n$ states, the intersection of $L$ and $R$ is either empty or contains a word shorter than…
We investigate the connection between properties of formal languages and properties of their generating series, with a focus on the class of holonomic power series. We first prove a strong version of a conjecture by Castiglione and…
We study programs with integer data, procedure calls and arbitrary call graphs. We show that, whenever the guards and updates are given by octagonal relations, the reachability problem along control flow paths within some language w1* ...…
Large language models (LMs) are currently trained to predict tokens given document prefixes, enabling them to directly perform long-form generation and prompting-style tasks which can be reduced to document completion. Existing pretraining…
Do language models (LMs) offer insights into human language learning? A common argument against this idea is that because their architecture and training paradigm are so vastly different from humans, LMs can learn arbitrary inputs as easily…
Classical mathematical models used in the semantics of programming languages and computation rely on idealized abstractions such as infinite-precision real numbers, unbounded sets, and unrestricted computation. In contrast, concrete…
We propose a scalable framework for deciding, proving, and explaining (in-)equivalence of context-free grammars. We present an implementation of the framework and evaluate it on large data sets collected within educational support systems.…
Program equivalence in linear contexts, where programs are used or executed exactly once, is an important issue in programming languages. However, existing techniques like those based on bisimulations and logical relations only target at…
To Rogers (1994) we owe the insight that monadic second order predicate logic with multiple successors (MSO) is well suited in many respects as a realistic formal base for syntactic theorizing. However, the agreeable formal properties of…
Given an input image, and nothing else, our method returns the bounding boxes of objects in the image and phrases that describe the objects. This is achieved within an open world paradigm, in which the objects in the input image may not…
The field of implicit complexity has recently produced several bounded-complexity programming languages. This kind of language allows to implement exactly the functions belonging to a certain complexity class. We here present a…
Large Language Models (LLMs) have benefited enormously from scaling, yet these gains are bounded by five fundamental limitations: (1) hallucination, (2) context compression, (3) reasoning degradation, (4) retrieval fragility, and (5)…
Classifying formal languages according to the expressiveness of grammars able to generate them is a fundamental problem in computational linguistics and, therefore, in the theory of computation. Furthermore, such kind of analysis can give…
We consider several novel aspects of unique factorization in formal languages. We reprove the familiar fact that the set uf(L) of words having unique factorization into elements of L is regular if L is regular, and from this deduce an…
Context-free languages can be characterized in several ways. This article studies projective linearisations of languages of simple dependency trees, i.e., dependency trees in which a node can govern at most one node with a given syntactic…
The height of a piecewise-testable language $L$ is the maximum length of the words needed to define $L$ by excluding and requiring given subwords. The height of $L$ is an important descriptive complexity measure that has not yet been…
Regular languages (RL) are the simplest family in Chomsky's hierarchy. Thanks to their simplicity they enjoy various nice algebraic and logic properties that have been successfully exploited in many application fields. Practically all of…
Recent work indicated that pretrained language models (PLMs) such as BERT and RoBERTa can be transformed into effective sentence and word encoders even via simple self-supervised techniques. Inspired by this line of work, in this paper we…