scholarly journals Using Transition Systems to Formalise Ideas from Vedanta

2021 ◽  
Author(s):  
Padmanabhan Krishnan
Keyword(s):  
Modal Logic ◽  
Computer Science ◽  
Theoretical Computer Science ◽  
Formal Description ◽  
Transition Systems ◽  
Theoretical Computer ◽  
Yoga Sutras

Vedanta is one of the oldest philosophical systems. While there are many detailed commentaries on Vedanta, there are very few mathematical descriptions of the different concepts developed there. This article shows how ideas from theoretical computer science can be used to explain Vedanta. The standard idea of transition systems and modal logic are used to develop a formal description for the different ideas in Vedanta. The generality of the formalism is illustrated via a number of examples including \samsara, \Patanjali's yoga sutras, karma, the three avasthas from the Mandukya Upanishad and the key difference between advaita and dvaita in relation to moksha.

scholarly journals Semantic Domains and Denotational Semantics

1989 ◽  
Vol 18 (276) ◽  
Author(s):  
Carl A. Gunter ◽  
Peter D. Mosses ◽  
Dana S. Scott
Keyword(s):  
Computer Science ◽  
Programming Language ◽  
Main Idea ◽  
Denotational Semantics ◽  
Mathematical Object ◽  
Theoretical Computer Science ◽  
Formal Description ◽  
Theoretical Computer ◽  
Language Semantics ◽  
Semantic Domains

<p>Denotational Semantics is a framework for the formal description of programming language semantics. The main idea of Denotational Semantics is that each phrase of the described language is given a <em>denotation</em>: a mathematical object that represents the contribution of the phrase to the meaning of any program in which it occurs. Moreover, the denotation of each phrase is determined just by the denotations of its subphrases.</p><p>This report consists of two chapters. The first, <em>Semantic Domains</em>, was written by Gunter and Scott. It is concerned with the <em>theory</em> of domains of denotations. The second, <em>Denotational Semantics</em>, was written by Mosses. It explains the formal notation used in denotational descriptions, and illustrates the major standard <em>technigues</em> for finding denotations of programming constructs.</p><p>Both chapters are to appear in the forthcoming <em>Handbook of Theoretical Computer Science</em> (North-Holland).</p>

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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