Related papers: On some impossible disentanglement puzzles

The aim of this work is to show how we can decompose a module (if decomposable) into an indecomposable module with the help of the minimization process.

The abelian sandpile model is a simple combinatorial model for critical behaviour which has the "abelian property" that the order in which we make moves does not change the final outcome of the game. This might seem to restrict the model's…

We show that constructible models of arbitrary complete continuous first-order theories are unique up to isomorphism.

For each Turing machine T, we construct an algebra A'(T) such that the variety generated by A'(T) has definable principal subcongruences if and only if T halts, thus proving that the property of having definable principal subcongruences is…

We built some congruences on semigroups, from where a decomposition of quasi-separative semigroups was obtained.

Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…

We compare some algebras appeared in the recent attempts to prove resolution of singularities in positive characteristic. We also construct an algebra which encodes the same information and it is equivalent, up to integral closure, to the…

We prove a strong non-structure theorem for a class of metric structures with an unstable pair of formulae. As a consequence, we show that weak categoricity (that is, categoricity up to isomorphisms and not isometries) implies several…

In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].

One of the most fundamental problems in tiling theory is the domino problem: given a set of tiles and tiling rules, decide if there exists a way to tile the plane using copies of tiles and following their rules. The problem is known to be…

Previous studies have used a specific success metric within an algorithmic search framework to prove machine learning impossibility results. However, this specific success metric prevents us from applying these results on other forms of…

We present in this paper a general algorithm for solving first-order formulas in particular theories called "decomposable theories". First of all, using special quantifiers, we give a formal characterization of decomposable theories and…

We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.

Jigsaw puzzle solving is an intriguing problem which has been explored in computer vision for decades. This paper focuses on a specific variant of the problem - solving puzzles with eroded boundaries. Such erosion makes the problem…

We study how equivalent nonisomorphic models of unsuperstable theories can be. We measure the equivalence by Ehrenfeucht-Fraisse games. This paper continues [HySh:474].

Computational indistinguishability is a key property in cryptography and verification of security protocols. Current tools for proving it rely on cryptographic game transformations. We follow Bana and Comon's approach, axiomatizing what an…

We investigate some properties of topological groups related to disconnectedness or Archimedeanness. We prove or disprove the preservation of those under operations as subgroups, quotients, products, etc. Characterizations of…

We provide some examples which give evidence to the conjectures contained in my paper "Finiteness of $p$-Divisible Sets of Multiple Harmonic Sums" (math.NT/0303043). All the main theoretical results can be found in that paper.

It is shown that the toy Turing Tumble, suitably extended with an infinitely long game board and unlimited supply of pieces, is Turing-Complete. This is achieved via direct simulation of a Turing machine. Unlike previously informally…

Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…