scholarly journals On the Prefix–Suffix Duplication Reduction

2020 ◽  
Vol 31 (01) ◽  
pp. 91-102
Author(s):  
Szilárd Zsolt Fazekas ◽  
Robert Mercaş ◽  
Daniel Reidenbach
Keyword(s):  
Computer Science ◽  
Theoretical Computer Science ◽  
Theoretical Computer ◽  
Square Roots ◽  
Context Free Language ◽  
Finite Set ◽  
Context Free ◽  
Free Language

This work answers some questions proposed by Bottoni, Labella, and Mitrana (Theoretical Computer Science 682, 2017) regarding the prefix–suffix reduction on words. The operation is defined as a reduction by one half of every square that is present as either a prefix or a suffix of a word, leading thus to a finite set of words associated to the starting one. The iterated case considers consecutive applications of the operations, on all the resulting words. We show that the classes of linear and context-free language are closed under iterated bounded prefix–suffix square reduction, and that for a given word we can determine in [Formula: see text] time all of its primitive prefix–suffix square roots.

scholarly journals Visualisation of Collage Grammar to CellWorks: ET0L Mode and Part Sensitive Mode

2017 ◽  
Vol 16 (3) ◽  
pp. 47-56
Author(s):  
Ann Susa Thomas
Keyword(s):  
Computer Science ◽  
Human Life ◽  
Three Dimensional ◽  
Theoretical Computer Science ◽  
Two Dimensional ◽  
Theoretical Computer ◽  
Finite Set ◽  
A Cell ◽  
Hyperedge Replacement ◽  
Better Than

Images are an important aspect of human life as one remembers pictures better than words. Informally, a twodimensional string is called a picture. A two-dimensional language (or picture language) is a set of pictures. Picture generation and analysis has become a widely investigated field in Theoretical Computer Science and in Mathematics. Collage grammars are studied as devices that generate pictures by rewriting based on hyperedge replacement. A cell-work is a finite set of cells where each cell (being a three dimensional entity) is surrounded by one or more faces. This paper focuses on how cell work languages can be captured by collage grammar in ET0L and Part Sensitive modes.

MORPHIC CHARACTERIZATIONS OF LANGUAGE FAMILIES IN TERMS OF INSERTION SYSTEMS AND STAR LANGUAGES

2011 ◽  
Vol 22 (01) ◽  
pp. 247-260 ◽  
Author(s):  
FUMIYA OKUBO ◽  
TAKASHI YOKOMORI
Keyword(s):  
Unique Feature ◽  
Recursively Enumerable ◽  
Context Free Language ◽  
Similar Characterization ◽  
Language L ◽  
Finite Set ◽  
Context Free ◽  
String Rewriting ◽  
Free Language ◽  
Recursively Enumerable Languages

Insertion systems have a unique feature in that only string insertions are allowed, which is in marked contrast to a variety of the conventional computing devices based on string rewriting. This paper will mainly focus on those systems whose insertion operations are performed in a context-free fashion, called context-free insertion systems, and obtain several characterizations of language families with the help of other primitive languages (like star languages) as well as simple operations (like projections, weak-codings). For each k ≥ 1, a language L is a k-star language if L = F+ for some finite set F with the length of each string in F is no more than k. The results of this kind have already been presented in [10] by Păun et al., while the purpose of this paper is to prove enhanced versions of them. Specifically, we show that each context-free language L can be represented in the form L = h(L(γ)∩F+), where γ is an insertion system of weight (3, 0) (at most three symbols are inserted in a context-free manner), h is a projection, and F+ is a 2-star language. A similar characterization can be obtained for recursively enumerable languages, where insertion systems of weight (3, 3) and 2-star languages are involved.

scholarly journals Optimization Over the Boolean Hypercube Via Sums of Nonnegative Circuit Polynomials

2021 ◽  
Author(s):  
Mareike Dressler ◽  
Adam Kurpisz ◽  
Timo de Wolff
Keyword(s):  
Computer Science ◽  
Affine Transformation ◽  
Optimization Problems ◽  
Polynomial Optimization ◽  
Theoretical Computer Science ◽  
Sums Of Squares ◽  
Theoretical Computer ◽  
Complexity Bounds ◽  
Polynomial Optimization Problems ◽  
Transformation Of Variables

AbstractVarious key problems from theoretical computer science can be expressed as polynomial optimization problems over the boolean hypercube. One particularly successful way to prove complexity bounds for these types of problems is based on sums of squares (SOS) as nonnegativity certificates. In this article, we initiate optimization problems over the boolean hypercube via a recent, alternative certificate called sums of nonnegative circuit polynomials (SONC). We show that key results for SOS-based certificates remain valid: First, for polynomials, which are nonnegative over the n-variate boolean hypercube with constraints of degree d there exists a SONC certificate of degree at most $$n+d$$ n + d . Second, if there exists a degree d SONC certificate for nonnegativity of a polynomial over the boolean hypercube, then there also exists a short degree d SONC certificate that includes at most $$n^{O(d)}$$ n O ( d ) nonnegative circuit polynomials. Moreover, we prove that, in opposite to SOS, the SONC cone is not closed under taking affine transformation of variables and that for SONC there does not exist an equivalent to Putinar’s Positivstellensatz for SOS. We discuss these results from both the algebraic and the optimization perspective.

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