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The Complexity of the Evaluation of Complex Algebra Expressions

1997
*
Journal of computer and system sciences (Print)
*

Similarly, NRA(powerset),

doi:10.1006/jcss.1997.1526
fatcat:lzmcm4r725ewnofx6weioz446i
*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 ...##
###
Simulation of the nested relational algebra by the flat relational algebra, with an application to the complexity of evaluating powerset algebra expressions

2001
*
Theoretical Computer Science
*

Our technique is also applied to partially answer a question posed by Suciu and Paredaens regarding

doi:10.1016/s0304-3975(99)00301-1
fatcat:h3tyftq7mrcuxdei4su6kgxroy
*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 ( ). ...##
###
Interactive Algorithms for the Verification of the Equality between Complex and Simplified Boolean-Algebra Expressions in Digital Decoders

2020
*
Review of Computer Engineering Research
*

Competing Interests:

doi:10.18488/journal.76.2020.71.27.37
fatcat:bayhfbostfhzxho7ix5z6dmvhm
*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*. ...##
###
Mathtalk: The design of an interface for reading algebra using speech
[chapter]

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. ...

##
###
Navigational XPath

2007
*
SIGMOD record
*

We survey

doi:10.1145/1328854.1328858
fatcat:kjouhgo2pnhftj26aj5vzovxhe
*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*? ...##
###
Neural Algebra of Classifiers
[article]

2018
*
arXiv
*
pre-print

Since these modules form a complete functional set, a classifier for any

arXiv:1801.08676v1
fatcat:mthjogpxw5fcnfk3yrxwvn3y4m
*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 ...##
###
From relation algebra to semi-join algebra

2017
*
Proceedings of The 16th International Symposium on Database Programming Languages - DBPL '17
*

As our main result, we show that each fragment

doi:10.1145/3122831.3122833
dblp:conf/dbpl/HellingsPGGW17
fatcat:4f2ytnvfprdc7le3e44kbp6njq
*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] . ...##
###
OUP accepted manuscript

2020
*
Computer journal
*

As our main result, we show that each fragment

doi:10.1093/comjnl/bxaa031
fatcat:ulnwq2b3sbeahgysmmtkzs6mvm
*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] . ...##
###
Finite Boolean Algebras for Solid Geometry using Julia's Sparse Arrays
[article]

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. ...

##
###
On the Complexity of Symbolic Computation

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

doi:10.1145/3476446.3535493
fatcat:s7lf53y6mnaknjpnnqi44nse6a
*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. ...##
###
Complexity of Mathematical Expressions and Its Application in Automatic Answer Checking

2021
*
Symmetry
*

In

doi:10.3390/sym13020188
fatcat:hicbhgb5t5bfzeglbr3n6bj7dm
*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. ...##
###
Symbolic Evaluation of Expressions from Racah's Algebra

2021
*
Symmetry
*

We here expand Jac,

doi:10.3390/sym13091558
fatcat:ux55mgexwngbva6hpmpv2muuv4
*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. ...##
###
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

2005
*
Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '05
*

This paper studies

doi:10.1145/1065167.1065179
dblp:conf/pods/Koch05
fatcat:posizfh6x5belellgsnsnovvpy
*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 ...##
###
On the complexity of nonrecursive XQuery and functional query languages on complex values

2006
*
ACM Transactions on Database Systems
*

This paper studies

doi:10.1145/1189769.1189771
fatcat:vfr7f25xebcjrj2i4xn255atsq
*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 ...
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