Related papers: Using Symbolic Computation to analyze some Childre…
Symbolic Computation algorithms and their implementation in computer algebra systems often contain choices which do not affect the correctness of the output but can significantly impact the resources required: such choices can benefit from…
Cirquent calculus is a proof system manipulating circuit-style constructs rather than formulas. Using it, this article constructs a sound and complete axiomatization CL16 of the propositional fragment of computability logic (the…
In this paper, a quantum variant of chess is introduced, which can be played on a traditional board, without using computers or other electronic devices. The rules of the game arise naturally by combining the rules of conventional chess…
This paper explores the cutting-edge Large Language Model with analytical reasoning on sports. Our analytical reasoning embodies the tasks of letting large language models count how many points each team scores in a quarter in the NBA and…
We present an algorithm that can efficiently compute a broad class of inferences for discrete-time imprecise Markov chains, a generalised type of Markov chains that allows one to take into account partially specified probabilities and other…
Markov chain Monte Carlo (MCMC) algorithms provide a very general recipe for estimating properties of complicated distributions. While their use has become commonplace and there is a large literature on MCMC theory and practice, MCMC users…
This paper applies probabilistic model checking techniques for discrete Markov chains to inference in Bayesian networks. We present a simple translation from Bayesian networks into tree-like Markov chains such that inference can be reduced…
In this note, I develop my personal view on the scope and relevance of symbolic computation in software science. For this, I discuss the interaction and differences between symbolic computation, software science, automatic programming,…
The present article is a brief informal survey of computability logic --- the game-semantically conceived formal theory of computational resources and tasks. This relatively young nonclassical logic is a conservative extension of classical…
There are few explicit examples of two player nonlocal games with a large gap between classical and quantum value. One of the reasons is that estimating the classical value is usually a hard computational task. This paper is devoted to…
Symbolic regression is a nonlinear regression method which is commonly performed by an evolutionary computation method such as genetic programming. Quantification of uncertainty of regression models is important for the interpretation of…
People can evaluate features of problems and their potential solutions well before we can effectively solve them. When considering a game we have never played, for instance, we might infer whether it is likely to be challenging, fair, or…
We looked at a method for estimating the complexity measure of game tree size (the number of legal games). It seems effective for a number of children's games such as Tic-Tac-Toe, Connect Four and Othello.
Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…
Consider a system of \(n\) players in which each initially starts on a different team. At each time step, we select an individual winner and an individual loser randomly and the loser joins the winner's team. The resulting Markov chain and…
Today, Machine Learning (ML) is of a great importance to society due to the availability of huge data and high computational resources. This ultimately led to the introduction of ML concepts at multiple levels of education including K-12…
Probabilistic program analysis aims to quantify the probability that a given program satisfies a required property. It has many potential applications, from program understanding and debugging to computing program reliability, compiler…
Weighted timed games are zero-sum games played by two players on a timed automaton equipped with weights, where one player wants to minimise the accumulated weight while reaching a target. Weighted timed games are notoriously difficult and…
There is a scalability gap between probabilistic and non-probabilistic verification. Probabilistic model checking tools are based either on explicit engines or on (Multi-Terminal) Binary Decision Diagrams. These structures are complemented…
In this paper, we introduce a system called GamePad that can be used to explore the application of machine learning methods to theorem proving in the Coq proof assistant. Interactive theorem provers such as Coq enable users to construct…