Deterministic Verification of Integer Matrix Multiplication in Quadratic Time
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F14%3A00425985" target="_blank" >RIV/67985807:_____/14:00425985 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-319-04298-5_33" target="_blank" >http://dx.doi.org/10.1007/978-3-319-04298-5_33</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-04298-5_33" target="_blank" >10.1007/978-3-319-04298-5_33</a>
Alternative languages
Result language
angličtina
Original language name
Deterministic Verification of Integer Matrix Multiplication in Quadratic Time
Original language description
Let A, B and C be n x n matrices of integer numbers. We show that there is a deterministic algorithm of quadratic time complexity (w.r.t. the number of arithmetical operations) verifying whether AB=C. For the integer matrices this result improves upon the best known result by Freivalds from 1977 that only holds for a randomized (Monte Carlo) algorithm. As a consequence, we design a quadratic time nondeterministic integer and rational matrix multiplication algorithm whose time complexity cannot be further improved. This indicates that any technique for proving a super-quadratic lower bound for deterministic matrix multiplication must exploit methods which would not work for the non-deterministic case.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
IN - Informatics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GAP202%2F10%2F1333" target="_blank" >GAP202/10/1333: NoSCoM: Non-Standard Computational Models and Their Applications in Complexity, Linguistics, and Learning</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
SOFSEM 2014. Theory and Practice of Computer Science
ISBN
978-3-319-04297-8
ISSN
0302-9743
e-ISSN
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Number of pages
8
Pages from-to
375-382
Publisher name
Springer
Place of publication
Cham
Event location
Nový Smokovec
Event date
Jan 26, 2014
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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