Related papers: The computational power of parsing expression gram…
We prove that every computably enumerable (c.e.) random real is provable in Peano Arithmetic (PA) to be c.e. random. A major step in the proof is to show that the theorem stating that "a real is c.e. and random iff it is the halting…
In a recently launched research program for developing logic as a formal theory of (interactive) computability, several very interesting logics have been introduced and axiomatized. These fragments of the larger Computability Logic aim not…
We describe an extension of Earley's parser for stochastic context-free grammars that computes the following quantities given a stochastic context-free grammar and an input string: a) probabilities of successive prefixes being generated by…
We observe that the vocabulary used to construct the "answer" to problems in computer algebra can have a dramatic effect on the computational complexity of solving that problem. We recall a formalization of this observation and explain the…
This note addresses the issue as to which ceers can be realized by word problems of computably enumerable (or, simply, c.e.) structures (such as c.e. semigroups, groups, and rings), where being realized means to fall in the same…
Probabilistic automata (PAs) have been successfully applied in formal verification of concurrent and stochastic systems. Efficient model checking algorithms have been studied, where the most often used logics for expressing properties are…
Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…
Language sciences rely less and less on formal syntax as their base. The reason is probably its lack of psychological reality, knowingly avoided. Philosophers of science call for a paradigm shift in which explanations are by mechanisms, as…
Computational models lie at the intersection of basic neuroscience and healthcare applications because they allow researchers to test hypotheses \textit{in silico} and predict the outcome of experiments and interactions that are very hard…
Covert speech involves imagining speaking without audible sound or any movements. Decoding covert speech from electroencephalogram (EEG) is challenging due to a limited understanding of neural pronunciation mapping and the low…
Spurred by the demand for interpretable models, research on eXplainable AI for language technologies has experienced significant growth, with feature attribution methods emerging as a cornerstone of this progress. While prior work in NLP…
Tree ensembles (TEs) find a multitude of practical applications. They represent one of the most general and accurate classes of machine learning methods. While they are typically quite concise in representation, their operation remains…
Language models (LM) are capable of remarkably complex linguistic tasks; however, numerical reasoning is an area in which they frequently struggle. An important but rarely evaluated form of reasoning is understanding probability…
Human reading behavior is tuned to the statistics of natural language: the time it takes human subjects to read a word can be predicted from estimates of the word's probability in context. However, it remains an open question what…
Mathematical language in scientific communications and educational scenarios is important yet relatively understudied compared to natural languages. Recent works on mathematical language focus either on representing stand-alone mathematical…
Concerning classical computational models able to express all the Primitive Recursive Functions (PRF), there are interesting results regarding limits on their algorithmic expressiveness or, equivalently, efficiency, namely the ability to…
Several popular language models represent local contexts in an input text $x$ as bags of words. Such representations are naturally encoded by a sequence graph whose vertices are the distinct words occurring in $x$, with edges representing…
This paper characterizes the inherent power of evolutionary algorithms. This power depends on the computational properties of the genetic encoding. With some encodings, two parents recombined with a simple crossover operator can sample from…
Automated theorem proving (ATP) has become an appealing domain for exploring the reasoning ability of the recent successful generative language models. However, current ATP benchmarks mainly focus on symbolic inference, but rarely involve…
How do language models "think"? This paper formulates a probabilistic cognitive model called the bounded pragmatic speaker, which can characterize the operation of different variations of language models. Specifically, we demonstrate that…