Related papers: A universal alphabet and rewrite system
This paper studies infinite graphs produced from a natural unfolding operation applied to finite graphs. Graphs produced via such operations are of finite degree and automatic over the unary alphabet (that is, they can be described by…
In the paper we can prove that every integer can be written as the sum of two integers, one perfect square and one squarefree. We also establish the asympotic formula for the number of representations of an integer in this form. The result…
Let $W$ be an infinite word over finite alphabet $A$. We get combinatorial criteria of existence of interval exchange transformations that generate the word W.
Algorithms to generate various combinatorial structures find tremendous importance in computer science. In this paper, we begin by reviewing an algorithm proposed by Rohl that generates all unique permutations of a list of elements which…
An automaton is called reachable if every state is reachable from the initial state. This notion has been generalized coalgebraically in two ways: first, via a universal property on pointed coalgebras, namely, that a reachable coalgebra has…
Neural network systems describe complex mappings that can be very difficult to understand. In this paper, we study the inverse problem of determining the input images that get mapped to specific neural network classes. Ultimately, we expect…
Artistic font generation aims to synthesize stylized glyphs based on a reference style. However, existing approaches suffer from limited style diversity and coarse control. In this work, we explore the potential of element-driven artistic…
In this paper we describe a data structure that supports pattern matching queries on a dynamically arriving text over an alphabet ofconstant size. Each new symbol can be prepended to $T$ in O(1) worst-case time. At any moment, we can report…
The recognition of unconstrained handwriting continues to be a difficult task for computers despite active research for several decades. This is because handwritten text offers great challenges such as character and word segmentation,…
In this paper we show how string rewriting methods can be applied to give a new method of computing double cosets. Previous methods for double cosets were enumerative and thus restricted to finite examples. Our rewriting methods do not…
The Binary Two-Up Sequence is the lexicographically earliest sequence of distinct nonnegative integers with the property that the binary expansion of the n-th term has no 1-bits in common with any of the previous floor(n/2) terms. We show…
We study the class of word-building games, where two players pick letters from a finite alphabet to construct a finite or infinite word. The outcome is determined by whether the resulting word lies in a prescribed set (a win for player $A$)…
We explain how a slight variant in the use of our recursive algorithm leads to improve the known lower bounds for the absolute trace of a totally positive algebraic integer. We also link the absolute trace of a totally positive algebraic…
Residue arithmetic is an elegant and convenient way of computing with integers that exceed the natural word size of a computer. The algorithms are highly parallel and hence naturally adapted to quantum computation. The process differs from…
A subspace of the space, L(n), of traceless complex $n\times n$ matrices can be specified by requiring that the entries at some positions $(i,j)$ be zero. The set, $I$, of these positions is a (zero) pattern and the corresponding subspace…
We show that the equality language of two non-periodic binary morphisms is generated by at most two words. If its rank is two, then the generators start (and end) with different letters. This in particular implies that any binary language…
Motivated by questions from program transformations, eight notions of isomorphisms between term rewriting systems are defined, analysed, and classified. The notions include global isomorphisms, where the renaming of variables and function…
e use Prolog as a flexible meta-language to provide executable specifications of some fundamental mathematical objects and their transformations. In the process, isomorphisms are unraveled between natural numbers and combinatorial objects…
In reactive synthesis, the goal is to automatically generate an implementation from a specification of the reactive and non-terminating input/output behaviours of a system. Specifications are usually modelled as logical formulae or automata…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…