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The Complexity of the Evaluation of Complex Algebra Expressions

Dan Suciu, Jan Paredaens
1997 Journal of computer and system sciences (Print)  
Similarly, NRA(powerset), the extension of NRA with powerset, has the same expressive power as the complex values algebra.  ...  We show that any other query in the algebra which expresses transitive closure needs exponential space, under a \call by value" evaluation strategy.  ...  Acknowledgments We would like to thank Val Tannen, Peter Buneman, and Jan Van den Bussche for their suggestions and support, Bart Kuijpers for carefully reading and commenting on the paper, and the reviewers  ... 
doi:10.1006/jcss.1997.1526 fatcat:lzmcm4r725ewnofx6weioz446i

Simulation of the nested relational algebra by the flat relational algebra, with an application to the complexity of evaluating powerset algebra expressions

Jan Van den Bussche
2001 Theoretical Computer Science  
Our technique is also applied to partially answer a question posed by Suciu and Paredaens regarding the complexity of evaluating powerset algebra expressions.  ...  Paredaens and Van Gucht proved that the at relational algebra has the same expressive power as the nested relational algebra, as far as queries over at relations and with at results are concerned.  ...  Complexity of evaluating powerset algebra expressions over unary relations The powerset algebra is the extension of the nested relational algebra with the powerset operator ( ).  ... 
doi:10.1016/s0304-3975(99)00301-1 fatcat:h3tyftq7mrcuxdei4su6kgxroy

Interactive Algorithms for the Verification of the Equality between Complex and Simplified Boolean-Algebra Expressions in Digital Decoders

Tochukwu Arinze Ikwunne, Samuel Obiora Okide
2020 Review of Computer Engineering Research  
Competing Interests: The authors declare that they have no competing interests. Acknowledgement: Both authors contributed equally to the conception and design of the study.  ...  However, the computational complexity of evaluating the equality of a complex Boolean algebra and its simplified form is still dissonant.  ...  Therefore, this work presents the use of novel algorithms in order to evaluate the equality between a simplified and complex Boolean algebra expression.  ... 
doi:10.18488/journal.76.2020.71.27.37 fatcat:bayhfbostfhzxho7ix5z6dmvhm

Mathtalk: The design of an interface for reading algebra using speech [chapter]

Robert Stevens, Alistair Edwards
1994 Lecture Notes in Computer Science  
The development and evaluation of Mathtalk has led to the proposal of a set of design principles that should facilitate the production of other, similar user interfaces for the reading of structured information  ...  Browsing functions and the associated command language allow the listening reader to shift his or her attention to any part of an expression.  ...  Acknowledgements We would like to thank John Local, Department of Linguistics, University of York for his help in the investigation of algebraic prosody.  ... 
doi:10.1007/3-540-58476-5_146 fatcat:rkt2ttudkzcfhezbzqzi5b7ko4

Navigational XPath

Balder ten Cate, Maarten Marx
2007 SIGMOD record  
We survey expressivity results for navigational fragments of XPath 1.0 and 2.0, as well as Regular XPath ≈ . We also investigate algebras for these fragments.  ...  Complexity of these algebras on trees We will now discuss the complexity of query evaluation and query containment for the four algebras interpreted on XML-trees (i.e., where the atomic relations are the  ...  Do the XPath dialect and the algebra have the same query containment and evaluation complexities?  ... 
doi:10.1145/1328854.1328858 fatcat:kjouhgo2pnhftj26aj5vzovxhe

Neural Algebra of Classifiers [article]

Rodrigo Santa Cruz, Basura Fernando, Anoop Cherian, Stephen Gould
2018 arXiv   pre-print
Since these modules form a complete functional set, a classifier for any complex visual concept defined as a boolean expression of primitives can be obtained by recursively applying the learned modules  ...  In this paper, we build on the compositionality principle and develop an "algebra" to compose classifiers for complex visual concepts.  ...  Acknowledgements: This research was supported by the Australian Research Council (ARC) through the Centre of Excellence for Robotic Vision (CE140100016) and was undertaken with the resources from the National  ... 
arXiv:1801.08676v1 fatcat:mthjogpxw5fcnfk3yrxwvn3y4m

From relation algebra to semi-join algebra

Jelle Hellings, Catherine L. Pilachowski, Dirk Van Gucht, Marc Gyssens, Yuqing Wu
2017 Proceedings of The 16th International Symposium on Database Programming Languages - DBPL '17  
As our main result, we show that each fragment of the relation algebras where intersection and/or di erence is only used on edges (and not on complex compositions) is expressively equivalent to a fragment  ...  This expressive equivalence holds for node queries that evaluate to sets of nodes.  ...  Complexity of rewritten expressions We consider the complexity of query evaluation in the usual framework [29] .  ... 
doi:10.1145/3122831.3122833 dblp:conf/dbpl/HellingsPGGW17 fatcat:4f2ytnvfprdc7le3e44kbp6njq

OUP accepted manuscript

2020 Computer journal  
As our main result, we show that each fragment of the relation algebras where intersection and/or di erence is only used on edges (and not on complex compositions) is expressively equivalent to a fragment  ...  This expressive equivalence holds for node queries that evaluate to sets of nodes.  ...  Complexity of rewritten expressions We consider the complexity of query evaluation in the usual framework [29] .  ... 
doi:10.1093/comjnl/bxaa031 fatcat:ulnwq2b3sbeahgysmmtkzs6mvm

Finite Boolean Algebras for Solid Geometry using Julia's Sparse Arrays [article]

Alberto Paoluzzi, Vadim Shapiro, Antonio DiCarlo, Giorgio Scorzelli, Elia Onofri
2020 arXiv   pre-print
The computational evaluation of every possible solid expression, usually denoted as CSG (Constructive Solid Geometry), is reduced to an equivalent logical expression of a finite set algebra over the cells  ...  We put forth a novel algebraic technique to evaluate any variadic expression between polyhedral d-solids (d = 2, 3) with regularized operators of union, intersection, and difference, i.e., any CSG tree  ...  Antonio Bottaro believed in this project and funded its development as responsible of R&D of Sogei (Italian Ministry of Economy and Finance) and CEO of the Geoweb subsidiary.  ... 
arXiv:1910.11848v3 fatcat:3okqlmuh2ncihjq2ha2vvk3ikm

On the Complexity of Symbolic Computation

Joris van der Hoeven
2022 Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation  
In this paper, we survey various basic and higher level tasks in computer algebra from the complexity perspective.  ...  Particular attention is paid to problems that are fundamental from this point of view and interconnections between other problems.  ...  The complexity of such algorithms can be expressed in terms of the number of evaluation points and the cost of conversions.  ... 
doi:10.1145/3476446.3535493 fatcat:s7lf53y6mnaknjpnnqi44nse6a

Complexity of Mathematical Expressions and Its Application in Automatic Answer Checking

Wei Su, Chuan Cai, Paul S. Wang, Hengjie Li, Zhen Huang, Qiang Huang
2021 Symmetry  
In the process of calculating the representation complexity of mathematical expressions, we transform the de bruijn notation into the binary lambda calculus of mathematical expressions that is inspired  ...  The complexity of a mathematical expression is a measure that can be used to compare the expression with other mathematical expressions and judge which one is simpler.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/sym13020188 fatcat:hicbhgb5t5bfzeglbr3n6bj7dm

Symbolic Evaluation of Expressions from Racah's Algebra

Stephan Fritzsche
2021 Symmetry  
We here expand Jac, the Jena Atomic Calculator, to facilitate the sum-rule evaluation of typical expressions from Racah's algebra.  ...  However, the use of Racah's algebra quickly leads to complex expressions, which are written in terms of generalized Clebsch–Gordan coefficients, Wigner n-j symbols, (tensor) spherical harmonics and/or  ...  Conflicts of Interest: The author declares no conflict of interest.  ... 
doi:10.3390/sym13091558 fatcat:ux55mgexwngbva6hpmpv2muuv4

Page 3447 of Mathematical Reviews Vol. , Issue 99e [page]

1999 Mathematical Reviews  
99e:68032 68P15 03D15 68Q15 Suciu, Dan; Paredaens, Jan (B-ANTW;; Wilrijk) The complexity of the evaluation of complex algebra expressions.  ...  For any powerset algebra expression f of the appropriate type, either for some m > 0 and for all n > 0, fim(tn) = f (rn), Or, for some c > 0, the space complexity of evaluating f(r,) is Q(2°") Since approximations  ... 

On the complexity of nonrecursive XQuery and functional query languages on complex values

Christoph Koch
2005 Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '05  
This paper studies the complexity of evaluating functional query languages for complex values such as monad algebra and the recursion-free fragment of XQuery.  ...  Then we study a fragment of XQuery, Core XQuery, that seems to incorporate all the features of a query language on complex values that are traditionally deemed essential.  ...  Monad algebra was shown expressively equivalent to a number of other important complex-value query languages such as nested relational algebra [26] and complex value algebra without powerset in previous  ... 
doi:10.1145/1065167.1065179 dblp:conf/pods/Koch05 fatcat:posizfh6x5belellgsnsnovvpy

On the complexity of nonrecursive XQuery and functional query languages on complex values

Christoph Koch
2006 ACM Transactions on Database Systems  
This paper studies the complexity of evaluating functional query languages for complex values such as monad algebra and the recursion-free fragment of XQuery.  ...  Then we study a fragment of XQuery, Core XQuery, that seems to incorporate all the features of a query language on complex values that are traditionally deemed essential.  ...  Monad algebra was shown expressively equivalent to a number of other important complex-value query languages such as nested relational algebra [26] and complex value algebra without powerset in previous  ... 
doi:10.1145/1189769.1189771 fatcat:vfr7f25xebcjrj2i4xn255atsq
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