相关论文: Modulo Three Problem With A Cellular Automaton Sol…

Separation is a classical problem asking whether, given two sets belonging to some class, it is possible to separate them by a set from a smaller class. We discuss the separation problem for regular languages. We give a Ptime algorithm to…

In this paper, we show how thread partitioning helps in proving properties of mobile systems. Thread partitioning consists in gathering the threads of a mobile system into several classes. The partitioning criterion is left as a parameter…

We show that all triples $(x_1,x_2,x_3)$ of singular moduli satisfying $x_1 x_2 x_3 \in \mathbb{Q}^{\times}$ are "trivial". That is, either $x_1, x_2, x_3 \in \mathbb{Q}$; some $x_i \in \mathbb{Q}$ and the remaining $x_j, x_k$ are distinct,…

Cellular automata are one-dimensional arrays of interconnected interacting finite automata. We investigate one of the weakest classes, the real-time one-way cellular automata, and impose an additional restriction on their inter-cell…

We propose a divisibility test for all integers which have 1, 3, 7 or 9 in their unit's place. In particular, then, the test applies for all prime divisors except 2 and 5.

In this paper, we propose an algorithm for the positive one-in-three satisfiability problem (Pos1in3SAT). The proposed algorithm can efficiently decide the existence of a satisfying assignment in all assignments for a given formula by using…

Odd numbers can be indexed by the map k(n)=(n-3)/2, n belonging to 2N+3. We first propose a basic primality test using this index function that was first introduced in article (8). Input size of operations is reduced which improves…

We show that $n$-bit integers can be factorized by independently running a quantum circuit with $\tilde{O}(n^{3/2})$ gates for $\sqrt{n}+4$ times, and then using polynomial-time classical post-processing. The correctness of the algorithm…

Abelian periodicity of strings has been studied extensively over the last years. In 2006 Constantinescu and Ilie defined the abelian period of a string and several algorithms for the computation of all abelian periods of a string were…

We address the separability problem for straight-line string constraints. The separability problem for languages of a class C by a class S asks: given two languages A and B in C, does there exist a language I in S separating A and B (i.e.,…

This paper presents efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with $\epsilon$-transitions. It gives an algorithm for testing the exponential ambiguity of an automaton $A$ in time…

We consider a class of finite state three-tape transducers which models the operation of shuffling and splitting words. We present them as automata over the so-called Shuffling Monoid. These automata can be seen as either shufflers or…

We investigate three combinatorial problems considered by Erd\"os, Rivat, Sark\"ozy and Sch\"on regarding divisibility properties of sum sets and sets of shifted products of integers in the context of function fields. Our results in this…

This paper presents the concept of digit polynomials, which leads to a deterministic and unconditional integer factorization algorithm with the runtime complexity $\mathcal{O}(N^{1/4+\epsilon})$. Strassen's well known factoring approach is…

For each integer $b \geq 3$ and every $x \geq 1$, let $\mathcal{N}_{b,0}(x)$ be the set of positive integers $n \leq x$ which are divisible by the product of their nonzero base $b$ digits. We prove bounds of the form $x^{\rho_{b,0} + o(1)}…

In this article, we try to explain and unify standard divisibility tests found in various books. We then look at recurring decimals, and list a few of their properties. We show how to compute the number of digits in the recurring part of…

We give a construction in a column of a one-dimensional cellular automaton of the Minkowski sum of two sets which can themselves occur in columns of cellular automata. It enables us to obtain another construction of the set of integers that…

In [6], a constraint on invariant measures of bi-permutative cellular automata has been observed: fixed values at the positive indices determine almost-surely a uniform conditional probability on the subset of values of positive conditional…

We consider the following "partition and sum" operation on a natural number: Treating the number as a long string of digits insert several plus signs in between some of the digits and carry out the indicated sum. This results in a smaller…

We give a possible explanation for the mystery of a missing number in the statement of a problem that asks for the non-negative integers to be partitioned into three subsets. We interpret the missing number as one of the clues that can lead…