scholarly journals Continuity of Partially Ordered Soft Sets via Soft Scott Topology and Soft Sobrification

2014 ◽  
Vol 9 ◽  
pp. 79-88
Author(s):  
A.F. Sayed
Keyword(s):  
Computer Science ◽  
Theoretical Computer Science ◽  
Soft Set ◽  
Domain Theory ◽  
Scott Topology ◽  
Soft Sets ◽  
Theoretical Computer ◽  
Partially Ordered ◽  
Completely Distributive ◽  
Characterization Theorems

This paper, based on the concept of partially ordered soft sets (possets, for short) which proposed by Tanay and Yaylali [23], we will give some other concepts which are developing the possets and helped us in obtaining a generalization of some important results in domain theory which has an important and central role in theoretical computer science. Moreover, We will establish some characterization theorems for continuity of possets by the technique of embedded soft bases and soft sobrification via soft Scott topology, stressing soft order properties of the soft Scott topology of possets and rich interplay between topological and soft order-theoretical aspects of possets. We will see that continuous possets are all embedded soft bases for continuous directed completely partially ordered soft set (i.e., soft domains), and vice versa. Thus, one can then deduce properties of continuous possets directly from the properties of continuous soft domains by treating them as embedded bases for continuous soft domains. We will see also that a posset is continuous if its soft Scott topology is a complete completely distributive soft lattice.

scholarly journals Topology, domain theory and theoretical computer science

1998 ◽  
Vol 89 (1-2) ◽  
pp. 3-59 ◽  
Author(s):  
Michael W. Mislove
Keyword(s):  
Computer Science ◽  
Theoretical Computer Science ◽  
Domain Theory ◽  
Theoretical Computer

scholarly journals Why doesn't ACM have a SIG for theoretical computer science?

2015 ◽  
Vol 58 (8) ◽  
pp. 5-5
Author(s):  
Moshe Y. Vardi
Keyword(s):  
Computer Science ◽  
Theoretical Computer Science ◽  
Theoretical Computer

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.

scholarly journals Contents and abstracts of the electronic notes in Theoretical Computer Science vol. 2

1998 ◽  
Vol 194 (1-2) ◽  
pp. 239-248
Author(s):  
Andrea Corradini ◽  
Ugo Montanari
Keyword(s):  
Computer Science ◽  
Theoretical Computer Science ◽  
Theoretical Computer
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