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Nowadays, technology has become dominant in the daily lives of most people around the world. From children to older people, technology is present, helping in the most diverse daily tasks and allowing accessibility. However, many times these…
Despite many recent advancements in language modeling, state-of-the-art language models lack grounding in the real world and struggle with tasks involving complex reasoning. Meanwhile, advances in the symbolic reasoning capabilities of AI…
The think-aloud method, where participants voice their thoughts as they solve a task, is a valuable source of rich data about human reasoning processes. Yet, it has declined in popularity in contemporary cognitive science, largely because…
Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random…
Predicting long-term outcomes of interventions is necessary for educational and social policy-making processes that might widely influence our society for the long-term. However, performing such predictions based on data from large-scale…
In the last ten years, the employment of symbolic methods has substantially extended both the theory and the applications of statistics and probability. This survey reviews the development of a symbolic technique arising from classical…
Teaching programming in early childhood (4-9) to enhance computational thinking has gained popularity in the recent movement of computer science for all. However, current practices ignore some fundamental issues resulting from young…
Dots-and-Boxes is a popular children's game whose winning strategies have been studied by Berlekamp, Conway, Guy, and others. In this article we consider two variations, Dots-and-Triangles and Dots-and-Polygons, both of which utilize the…
Neural reasoning accuracy improves when generating intermediate reasoning steps. However, the source of this improvement is yet unclear. Here, we investigate and factorize the benefit of generating intermediate steps for symbolic reasoning.…
Recent empirical work has shown that human children are adept at learning and reasoning with probabilities. Here, we model a recent experiment investigating the development of school-age children's non-symbolic probability reasoning ability…
This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compresses it to a much smaller matrix by multiplying it by a…
Figurative drawing is a skill that takes time to learn, and evolves during different childhood phases that begin with scribbling and end with representational drawing. Between these phases, it is difficult to assess when and how children…
Symbolic mathematical computing systems have served as a canary in the coal mine of software systems for more than sixty years. They have introduced or have been early adopters of programming language ideas such ideas as dynamic memory…
Playing games is inherently human, and a lot of games are created to challenge different human characteristics. However, these tasks are often left out when evaluating the human-like nature of artificial models. The objective of this work…
The present paper introduces a novel notion of `(effective) computability', called viability, of strategies in game semantics in an intrinsic (i.e., without recourse to the standard Church-Turing computability), non-inductive and…
This article is a tutorial on Markov chain Monte Carlo simulations and their statistical analysis. The theoretical concepts are illustrated through many numerical assignments from the author's book on the subject. Computer code (in Fortran)…
Chain of Thought (CoT) of multi-step benefits from the logical structure of the reasoning steps and task-specific actions, significantly enhancing the mathematical reasoning capabilities of large language models. As the prevalence of long…
A cost Markov chain is a Markov chain whose transitions are labelled with non-negative integer costs. A fundamental problem on this model, with applications in the verification of stochastic systems, is to compute information about the…
A chessboard has the property that every row and every column has as many white squares as black squares. In this mostly methodological note, we address the problem of counting such rectangular arrays with a fixed (numeric) number of rows,…
There exists a well-known hook-length formula for calculating the dimensions of 2D Young diagrams. Unfortunately, the analogous formula for 3D case is unknown. We introduce an approach for calculating the estimations of dimensions of…