Related papers: A Mathematical Proof of Dodgson's Algorithm
A Lagrange Theorem in dimension 2 is proved, for a particular two-dimensional algorithm, with a very natural geometrical definition. Dirichlet-type properties for the convergence of the algorithm are also proved. These properties procced…
We provide elementary proofs of several results concerning the possible outcomes arising from a fixed profile within the class of positional voting systems. Our arguments enable a simple and explicit construction of paradoxical profiles,…
We present a ``method'' for bijective proofs for determinant identities, which is based on translating determinants to Schur functions by the Jacobi--Trudi identity. We illustrate this ``method'' by generalizing a bijective construction…
It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…
We propose an algorithm that test membership for regular expressions and show that the algorithm is correct. This algorithm is written in the style of a sequent proof system. The advantage of this algorithm over traditional ones is that the…
The automated generation of exercises may substantially reduce the time educators devote to manual exercise design. A major obstacle to the integration of such automation into teaching practice, however, lies in the ability to control the…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
This paper argues that automated proofs of identities for non-terminating hypergeometric series are feasible by a combination of Zeilberger's algorithm and asymptotic estimates. For two analogues of Saalsch\"utz' summation formula in the…
Using multisets, we develop novel techniques for mechanizing the proofs of the synthesis conjectures for list-sorting algorithms, and we demonstrate them in the Theorema system. We use the classical principle of extracting the algorithm as…
A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
The purpose of this note is to prove the existence of a randomized mechanism, a social decision scheme (SDS), with desirable fairness, efficiency, and strategyproofness properties unmatched by all known SDSs. In particular, we disprove a…
We employ computer algebra algorithms to prove a collection of identities involving Bessel functions with half-integer orders and other special functions. These identities appear in the famous Handbook of Mathematical Functions, as well as…
We consider the problem of explaining the predictions of an arbitrary blackbox model $f$: given query access to $f$ and an instance $x$, output a small set of $x$'s features that in conjunction essentially determines $f(x)$. We design an…
We give an endorsement for Cornacchia's famous algorithm. Thus we do not claim anything new but an approach which is supposed to be simpler than those of previous works written with the same aim.
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…
Probabilistic algorithms are applied to prove theorems about the finite general linear and unitary groups which are typically proved by techniques such as character theory and Moebius inversion. Among the theorems studied are Steinberg's…
We consider systems of recursively defined combinatorial structures. We give algorithms checking that these systems are well founded, computing generating series and providing numerical values. Our framework is an articulation of the…
This paper deals with a method for solving Poisson Equation (PE) based on genetic algorithms and grammatical evolution. The method forms generations of solutions expressed in an analytical form. Several examples of PE are tested and in most…