Related papers: Coins and Logic
This note highlights an interesting connection between Euler sums of even weight and prime numbers.
On the blockchain, NFT games have risen in popularity, spawning new types of digital assets. We present a simplified version of well-known NFT games, followed by a discussion of issues influencing the structure and stability of generic…
Analogy has been shown to be important in many key cognitive abilities, including learning, problem solving, creativity and language change. For cognitive models of analogy, the fundamental computational question is how its inherent…
This paper presents a solution to the Knights and Spies Problem: In a room there are n people, each labelled with a unique number between 1 and n. A person may either be a knight or a spy. Knights always tell the truth, while spies may…
Weighted programs generalize probabilistic programs and offer a framework for specifying and encoding mathematical models by means of an algorithmic representation. Kleene algebra with tests is an algebraic formalism based on regular…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
In answer set programming, two groups of rules are considered strongly equivalent if they have the same meaning in any context. Strong equivalence of two programs can be sometimes established by deriving rules of each program from rules of…
In this paper, we will present an algorithm to resolve the counterfeit coins problem in the case that the number of false coins is unknown in advance.
Reinforcement learning with verifiable rewards (RLVR) is a promising approach for training large language models (LLMs) with stronger reasoning abilities. It has also been applied to a variety of logic puzzles. In this work, we study the…
These notes describe some results on dice comparisons when changing the numbers on the faces while the sum of all the face stay the same.
In this paper, we present a board game: Square War. The game definition of Square War is similar to the classic Chinese board game Go. Then we propose a mathematical problem of the game Square War. Finally, we show that the problem can be…
In the spirit of "multi-culturalism", we use four kinds of computations: simulation, numeric, symbolic, and "conceptual" to explore some "games of pure chance" inspired by children board games like "Snakes and Ladders" (aka as "Chutes and…
In this note we prove a weighted version of the Khintchine inequalities.
We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.
Numberlink is a puzzle game in which players are given a grid with nodes marked with a natural number, $n$, and asked to create $n$ connections with neighboring nodes. Connections can only be made with top, bottom, left and right neighbors,…
We study counting propositional logic as an extension of propositional logic with counting quantifiers. We prove that the complexity of the underlying decision problem perfectly matches the appropriate level of Wagner's counting hierarchy,…
We show that a proof in multiplicative linear logic can be represented as a decorated surface, such that two proofs are logically equivalent just when their surfaces are geometrically equivalent. This is an extended abstract for…
This is an expository article of our work on analogies between knot theory and algebraic number theory. We shall discuss foundational analogies between knots and primes, 3-manifolds and number rings mainly from the group-theoretic point of…
Consider a periodical (in two independent directions) tiling of the plane with polygons (faces). In this article we shall only give examples using squares, regular hexagons, equilateral triangles and parallelograms ("unions" of two…
We prove computational intractability of variants of checkers: (1) deciding whether there is a move that forces the other player to win in one move is NP-complete; (2) checkers where players must always be able to jump on their turn is…