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Counting distinct permutations with replacement, especially when involving multiple subwords, is a longstanding challenge in combinatorial analysis, with critical applications in cryptography, bioinformatics, and statistical modeling. This…
We show that lambda calculus is a computation model which can step by step simulate any sequential deterministic algorithm for any computable function over integers or words or any datatype. More formally, given an algorithm above a family…
We investigate the special class of formulas made up of arbitrary but finite com- binations of addition, multiplication, and exponentiation gates. The inputs to these formulas are restricted to the integral unit 1. In connection with such…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
This study introduces SECODA, a novel general-purpose unsupervised non-parametric anomaly detection algorithm for datasets containing continuous and categorical attributes. The method is guaranteed to identify cases with unique or sparse…
Encryption-based attacks have introduced significant challenges for detection mechanisms that rely on predefined signatures, heuristic indicators, or static rule-based classifications. Probabilistic Latent Encryption Mapping presents an…
We propose an ensemble algorithm, which provides a new approach for evaluating and summing up a set of function samples. The proposed algorithm is not a quantum algorithm, insofar it does not involve quantum entanglement. The query…
Automated deduction lies at the core of Artificial Intelligence (AI), underpinning theorem proving, formal verification, and logical reasoning. Despite decades of progress, reconciling deductive completeness with computational efficiency…
We propose a novel system, MathMistake Checker, designed to automate step-by-step mistake finding in mathematical problems with lengthy answers through a two-stage process. The system aims to simplify grading, increase efficiency, and…
Spreadsheets are one of the most widely used programming environments, and are widely deployed in domains like finance where errors can have catastrophic consequences. We present a static analysis specifically designed to find spreadsheet…
A number of automated techniques and tools were proposed in the research literature over the years which aim to support the spreadsheet developer in the process of testing and debugging a faulty spreadsheet. One underlying assumption of…
Venkatachala on the one hand, and Avdispahi\'c & Zejnulahi on the other, both studiied integer sequences with an unusual sum property defined in a greedy way, and proved many results about them. However, their proofs were rather lengthy and…
Windowed recurrences are sliding window calculations where a function is applied iteratively across the window of data, and are ubiquitous throughout the natural, social, and computational sciences. In this monograph we explore the…
This paper presents the first step of a wider research effort to apply tree automata completion to the static analysis of functional programs. Tree Automata Completion is a family of techniques for computing or approximating the set of…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
Understanding complex phenomena often requires analyzing high-dimensional data to uncover emergent properties that arise from multifactorial interactions. Here, we present EMUSES (Emerging-properties Mapping Using Spatial Embedding…
We illustrate the power of Experimental Mathematics and Symbolic Computation to suggest irrationality proofs of natural constants, and the determination of their irrationality measures. Sometimes such proofs can be fully automated, but…
Nested sampling (NS) is a popular algorithm for Bayesian computation. We investigate statistical errors in NS both analytically and numerically. We show two analytic results. First, we show that the leading terms in Skilling's expression…
In this article we will use Minecraft to experimentally approximate the values of four different mathematical constants. The mathematical constants that we will approximate are $\sqrt{2}, \pi$, Euler's number $e$, and Ap\'{e}ry's constant…
Mathematical expressions (MEs) have complex two-dimensional structures in which symbols can be present at any nested depth like superscripts, subscripts, above, below etc. As MEs are represented using LaTeX format, several text retrieval…