Related papers: Quantitative Language Automata
We explore language semantics for automata combining probabilistic and nondeterministic behavior. We first show that there are precisely two natural semantics for probabilistic automata with nondeterminism. For both choices, we show that…
Q# is a standalone domain-specific programming language from Microsoft for writing and running quantum programs. Like most industrial languages, it was designed without a formal specification, which can naturally lead to ambiguity in its…
We define guarded variable automata (GVAs), a simple extension of finite automata over infinite alphabets. In this model the transitions are labelled by letters or variables ranging over an infinite alphabet and guarded by conjunction of…
To use generative question-and-answering (QA) systems for decision-making and in any critical application, these systems need to provide well-calibrated confidence scores that reflect the correctness of their answers. Existing calibration…
The natural Hilbert Space of quantum particles can implement maximum-likelihood (ML) decoding of classical information. The 'Quantum Product Algorithm' (QPA) is computed on a Factor Graph, where function nodes are unitary matrix operations…
In the realm of education, student evaluation holds equal significance to imparting knowledge. To be evaluated, students usually need to go through text-based academic assessment methods. Instructors need to make a diverse set of questions…
Large Language Models (LLMs) are often described as instances of foundation models that possess strong generalization obeying scaling laws, and therefore transfer robustly across various conditions in few- or zero-shot manner. Such claims…
This paper investigates the ability of artificial neural networks to judge the grammatical acceptability of a sentence, with the goal of testing their linguistic competence. We introduce the Corpus of Linguistic Acceptability (CoLA), a set…
The past research on the state complexity of operations on regular languages is examined, and a new approach based on an old method (derivatives of regular expressions) is presented. Since state complexity is a property of a language, it is…
Unsupervised commonsense question answering is appealing since it does not rely on any labeled task data. Among existing work, a popular solution is to use pre-trained language models to score candidate choices directly conditioned on the…
Query auto completion (QAC) systems are a standard part of search engines in industry, helping users formulate their query. Such systems update their suggestions after the user types each character, predicting the user's intent using…
An infinite permutation $\alpha$ is a linear ordering of $\mathbb N$. We study properties of infinite permutations analogous to those of infinite words, and show some resemblances and some differences between permutations and words. In this…
Let L be an infinite regular language on a totally ordered alphabet (A,<). Feeding a finite deterministic automaton (with output) with the words of L enumerated lexicographically with respect to < leads to an infinite sequence over the…
This paper concerns quasi-stochastic approximation (QSA) to solve root finding problems commonly found in applications to optimization and reinforcement learning. The general constant gain algorithm may be expressed as the…
This article contains ideas and their elaboration for quantifiers, which appeared after checking in practice the experimental language of the formal knowledge representation YAFOLL [1]: - looking at for_all and exists quantifiers as…
Vision-Language-Action (VLA) models are emerging as a promising paradigm for end-to-end autonomous driving, valued for their potential to leverage world knowledge and reason about complex driving scenes. However, existing methods suffer…
The value 1 problem is a decision problem for probabilistic automata over finite words: given a probabilistic automaton A, are there words accepted by A with probability arbitrarily close to 1? This problem was proved undecidable recently.…
Large language models (LLMs) are advanced artificial intelligence (AI) systems that can perform a variety of tasks commonly found in human intelligence tests, such as defining words, performing calculations, and engaging in verbal…
This paper introduces a formal metalanguage called the lambda-q calculus for the specification of quantum programming languages. This metalanguage is an extension of the lambda calculus, which provides a formal setting for the specification…
Regular languages -- the languages accepted by deterministic finite automata -- are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we…