Related papers: Cyclotomy Primality Proofs and their Certificates
We introduce a sound and complete coinductive proof system for reachability properties in transition systems generated by logically constrained term rewriting rules over an order-sorted signature modulo builtins. A key feature of the…
We present a new proof of a primality criterion first proved by Emmanuel Vantieghem.
We study an LCM-based analogue of Rowland's GCD-based prime-generating recurrence, introduced by the author in 2008. The multiplicative increments of this sequence are conjectured always to be $1$ or prime, but a complete proof requires a…
In this paper, we introduce two primality tests based on new divisibility properties of binomial coefficients. These new properties were enunciated and proved in previous work. We also study two similar tests that can be obtained from…
We consider first passage percolation (FPP) with passage times generated by a general class of models with long-range correlations on $\mathbb{Z}^d$, $d\geq 2$, including discrete Gaussian free fields, Ginzburg-Landau $\nabla \phi$…
This paper studies the first passage percolation (FPP) model: each edge in the cubic lattice is assigned a random passage time, and consideration is given to the behavior of the percolation region $B(t)$, which consists of those vertices…
When proving the correctness of a method for slicing probabilistic programs, it was previously discovered by the authors that for a fixed point iteration to work one needs a non-standard starting point for the iteration. This paper presents…
Cyclic codes are an interesting type of linear codes and have applications in communication and storage systems due to their efficient encoding and decoding algorithms. They have been studied for decades and a lot of progress has been made.…
G. Cz\'edli and E.\,T. Schmidt introduced in 2012 the fork extension. Continuing from Part I, we investigate the congruences of a fork extension. This paper has been merged with Part I, under the title Congruences of fork extensions of slim…
We recall the motivations for the Compositeness Standard Model(CSM) concept, its precise description, the procedures for its applications and the particular constraints that it requires. We present its most spectacular predictions for…
In the first article of this series we have presented the history of auxiliary primes from Legendre's proof of the quadratic reciprocity law up to Artin's reciprocity law. We have also seen that the proof of Artin's reciprocity law consists…
We study induction on the program structure as a proof method for bisimulation-based compiler correctness. We consider a first-order language with mutually recursive function definitions, system calls, and an environment semantics. The…
A cyclic proof system, called CLKID-omega, gives us another way of representing inductive definitions and efficient proof search. The 2005 paper by Brotherston showed that the provability of CLKID-omega includes the provability of LKID,…
Although a deterministic polytime algorithm for primality testing is now known, the Rabin-Miller randomized test of primality continues being the most efficient and widely used algorithm. We prove the correctness of the Rabin-Miller…
We study the ring of invariants for a finite dimensional representation $V$ of the group $C_2$ of order 2 in characteristic $2$. Let $\sigma$ denote a generator of $C_2$ and $\{x_1,y_1 \dots, x_m,y_m\}$ a basis of $V^*$. Then $\sigma(x_i) =…
Proofs of coherence in category theory, starting from Mac Lane's original proof of coherence for monoidal categories, are sometimes based on confluence techniques analogous to what one finds in the lambda calculus, or in term-rewriting…
The aim of this note is a proof of a recent conjecture of Kellner concerning the number of distinct prime factors of a particular product of primes. The proof uses profound results from analytic number theory, such as Granville-Ramar\'{e}'s…
An efficient entailment proof system is essential to compositional verification using separation logic. Unfortunately, existing decision procedures are either inexpressive or inefficient. For example, Smallfoot is an efficient procedure but…
By adapting Salomaa's complete proof system for equality of regular expressions under the language semantics, Milner (1984) formulated a sound proof system for bisimilarity of regular expressions under the process interpretation he…
We propose an algorithm determining the primality of numbers $M=Ap^n+w_n$ where $w_n^{p-1}\equiv1\pmod{p^n}$ and $A<p^n$ and give example when $p=7$. $p$ th reciprocity law is involved. The algorithm runs in polynomial time in $\log_2(M)$…