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Lower Bounds and PIT for Non-Commutative Arithmetic Circuits with Restricted Parse Trees *

Kim Larsen, Hans Bodlaender, Jean-Francois Raskin
2017 14 Leibniz International Proceedings in Informatics Schloss Dagstuhl-Leibniz-Zentrum für Informatik   unpublished
Such restrictions capture essentially all non-commutative circuit models for which lower bounds are known. We prove several results about such circuits. 1.  ...  We show explicit exponential lower bounds for circuits with up to an exponential number of parse trees, strengthening the work of Lagarde, Malod, and Perifel (ECCC 2016), who prove such a result for Unique  ...  d ≤ log n). 41:4 Non-Commutative Arithmetic Circuits with Restricted Parse Trees Finally, we consider the Polynomial Identity Testing (PIT) problem for non-commutative circuits with restricted parse  ... 
fatcat:ctniibep5ja2hivzaies54rwmq

Quasipolynomial Hitting Sets for Circuits with Restricted Parse Trees

Ramprasad Saptharishi, Anamay Tengse, Michael Wagner
2018 Foundations of Software Technology and Theoretical Computer Science  
We study the class of non-commutative Unambiguous circuits or Unique-Parse-Tree (UPT) circuits, and a related model of Few-Parse-Trees (FewPT) circuits (which were recently introduced by Lagarde, Malod  ...  size for FewPT circuits (circuits with constantly many parse tree shapes), An explicit hitting set of polynomial size for UPT circuits (of known parse tree shape), when a parameter of preimage-width is  ...  Acknowledgements We thank the organizers of the NMI Workshop on Arithmetic Complexity 2017 where we learned of the circuit classes that we study in this paper.  ... 
doi:10.4230/lipics.fsttcs.2018.6 dblp:conf/fsttcs/SaptharishiT18 fatcat:lad7cqooujegtg7lkyobavnhyu

Lower Bounds for Arithmetic Circuits via the Hankel Matrix

Nathanaël Fijalkow, Guillaume Lagarde, Pierre Ohlmann, Olivier Serre, Markus Bläser, Christophe Paul
2020 Symposium on Theoretical Aspects of Computer Science  
Previous superpolynomial lower bounds were known for circuits with up to 2^{d^{1/3-ε}} parse trees, for any ε > 0.  ...  We show a superpolynomial lower bound for circuits with up to 2^{d^{1/3 - ε}} parse trees, for any ε > 0. When d is polylogarithmic in n, we push this further to up to 2^{d^{1 - ε}} parse trees.  ...  Indeed, in the commutative setting, Lemma 21 holds as such (with a shape being an element of T d , that is, a commutative parse tree of size d).  ... 
doi:10.4230/lipics.stacs.2020.24 dblp:conf/stacs/FijalkowLOS20 fatcat:s3fdiku2rnfojlaso46kd4haeu

Non-commutative computations: lower bounds and polynomial identity testing [article]

Guillaume Lagarde, Guillaume Malod, Sylvain Perifel
2016 Electronic colloquium on computational complexity  
In the setting of non-commutative arithmetic computations, we define a class of circuits that generalize algebraic branching programs (ABP).  ...  Generalizing a result of Nisan [17] on ABPs, we provide an exact characterization of the complexity of any polynomial in our model, and use it to prove exponential lower bounds for explicit polynomials  ...  Very little progress was made for a long time, and there is still no known lower bound for general non-commutative arithmetic circuits that is stronger than those that we already have for general commutative  ... 
dblp:journals/eccc/LagardeMP16 fatcat:5x223fhj2rcddbfuooeyut4upi

Quasi-polynomial Hitting Sets for Circuits with Restricted Parse Trees [article]

Ramprasad Saptharishi, Anamay Tengse
2017 arXiv   pre-print
We study the class of non-commutative Unambiguous circuits or Unique-Parse-Tree (UPT) circuits, and a related model of Few-Parse-Trees (FewPT) circuits (which were recently introduced by Lagarde, Malod  ...  of quasipolynomial size for FewPT circuits (circuits with constantly many parse tree shapes), (3) An explicit hitting set of polynomial size for UPT circuits (of known parse tree shape), when a parameter  ...  Acknowledgements We thank the organizers of the NMI Workshop on Arithmetic Complexity 2017 where we learned of the circuit classes that we study in this paper.  ... 
arXiv:1709.03068v2 fatcat:mqftewbdmfglxlddbiy7lx2sje

Efficient Identity Testing and Polynomial Factorization over Non-associative Free Rings [article]

V. Arvind, Rajit Datta, Partha Mukhopadhyay, S. Raja
2017 arXiv   pre-print
Prior to this work, nonassociative arithmetic computation was considered by Hrubes, Wigderson, and Yehudayoff [HWY10], and they showed lower bounds and proved completeness results.  ...  Our result is obtained by a suitable adaptation of the PIT algorithm of Raz-Shpilka [RS05] for noncommutative ABPs. (2) Given an arithmetic circuit C of size s computing a polynomial f∈F{x_1,x_2,...  ...  We also note that in [AR16] an exponential lower bound is shown for set-multilinear arithmetic circuits with the additional semantic constraint that each monomial has a unique parse tree in the circuit  ... 
arXiv:1705.00140v2 fatcat:k7cermilhzawhn6qhcwlvbtwle

Efficient Identity Testing and Polynomial Factorization in Nonassociative Free Rings

Vikraman Arvind, Rajit Datta, Partha Mukhopadhyay, S. Raja, Marc Herbstritt
2017 International Symposium on Mathematical Foundations of Computer Science  
Prior to this work, nonassociative arithmetic computation was considered by Hrubes, Wigderson, and Yehudayoff [7], and they showed lower bounds and proved completeness results.  ...  Given an arithmetic circuit C of size s computing a polynomial f ∈ F{x 1 , x 2 , . . . , x n } of degree d, we give an efficient deterministic algorithm to compute circuits for the irreducible factors  ...  We also note that in [4] an exponential lower bound is shown for set-multilinear arithmetic circuits with the additional semantic constraint that each monomial has a unique parse tree in the circuit  ... 
doi:10.4230/lipics.mfcs.2017.38 dblp:conf/mfcs/ArvindDM017 fatcat:ehe7e6qbcrdljbtc6rltwaydaa

On Probabilistic Checking in Perfect Zero Knowledge [article]

Eli Ben-Sasson and Alessandro Chiesa and Michael A. Forbes and Ariel Gabizon and Michael Riabzev and Nicholas Spooner
2016 arXiv   pre-print
, and consists of detecting dual constraints with polynomial support size for codes of exponential block length.  ...  The complexity class #P has PZK proofs in the model of Interactive PCPs (IPCPs) [KR08], where the verifier first receives from the prover a PCP and then engages with the prover in an Interactive Proof  ...  for Theoretical Computer Science.  ... 
arXiv:1610.03798v1 fatcat:xgmkxf4tavf2bgw3flgzu5ssre

On the Partial Derivative Method Applied to Lopsided Set-Multilinear Polynomials

Nutan Limaye, Srikanth Srinivasan, Sébastien Tavenas, Shachar Lovett
2022
This shows a stronger formula lower bound of N^{Ω(d^{1/4})} for set-multilinear formulas of product-depth 3, and also puts a non-trivial constraint on the best lower bounds we can hope to prove at th [  ...  We make progress on understanding a lower bound technique that was recently used by the authors to prove the first superpolynomial constant-depth circuit lower bounds against algebraic circuits.  ...  We would also like to thank Niranjan Balachandran for his comments and an alternate proof of a combinatorial lemma in the paper, and Swastik Kopparty and Shachar Lovett for discussions.  ... 
doi:10.4230/lipics.ccc.2022.32 fatcat:mqiowkzffnbe3ljzwdlne6zsuq

Unconditional Lower Bounds in Complexity Theory

Igor Carboni Oliveira
2017
Further, we establish a strong round-separation theorem for bounded-depth circuits, showing that (r+1)-round protocols can be substantially more efficient than r-round protocols, for every r ∈ ℕ.  ...  We prove that the communication complexity of the Majority function on n-bit inputs with respect to Boolean circuits of size s and depth d extended with modulo p gates is precisely n/log^{ϴ(d)} s, where  ...  Chapters 3 and 4 provide strong lower bounds for restricted classes of Boolean circuits.  ... 
doi:10.7916/d8zp45kt fatcat:3qizieqkfrfhhezeevmdp5bcom

Comparative Analysis of Different Machine Learning Classifiers for the Prediction of Chronic Diseases [chapter]

Rajesh Singh, Anita Gehlot, Dharam Buddhi
2022 Comparative Analysis of Different Machine Learning Classifiers for the Prediction of Chronic Diseases  
Chronic Diseases are the most dangerous diseases for humans and have significant effects on human life. Chronic Diseases like heart disease & Diabetes are the main causes of death.  ...  Precise diagnosis of these diseases on time is very significant for maintaining a healthy life.  ...  The performance of existing and proposed algorithms is analysed with regard to several metrics.  ... 
doi:10.13052/rp-9788770227667 fatcat:da47mjbbyzfwnbpde7rgbrlppe

Latent Immunological Effects of Gestational Exposure to Heptachlor Epoxide

Dean Baker, Haiou Yang, Ulrike Luderer, Sastry Gollapudi
2011 Epidemiology  
Methods: Using case-series analysis, daily morbidity and mortality rates during heatwaves were compared with rates during non-heatwave periods within the respective years and restricted to the warm season  ...  Extreme exposure to heat is associated with higher death rates in people with lower age, compared to a rise in temperature.  ...  We used multiple linear regression to investigate the association of exposure to traffic noise with CAC, controlling for gender, age, education, occupation, smoking, waist-hip ratio, physical activity,  ... 
doi:10.1097/01.ede.0000392128.65234.11 fatcat:dft32xujtzchzcnldns7ppf6iq

Robotic isotropy and optimal robot design of planar manipulators

M.V. Kircanski
Proceedings of the 1994 IEEE International Conference on Robotics and Automation  
Top-down and Bottom-up Parsing Techniques. Recursive Descent Parsing. LL (1) Parsing. LALR Parsing and Operator Precedence Parsing. LEX and YACC.  ...  Context Free Grammars And Push Down Automata: Context Free Grammars and Languages, Parse Trees, CNF and GNF, Pumping Lemma, Closure properties; Push Down Automata, Concept of Stack, PDA for CFG.  ...  Locating and improving machines with substandard performance. The importance of lap preparation and the technological considerations involved.  ... 
doi:10.1109/robot.1994.351213 dblp:conf/icra/Kircanski94 fatcat:uawqnzropbgivcanzqihtimt2m

AN APPLICATION OF THE 5-S ACTIVITY THEORETIC REQUIREMENTS METHOD
english

2006 Proceedings of the First International Conference on Software and Data Technologies   unpublished
IS-6 more aligned with (better suited for) loosely coupled integration. This is because data can be easily put aside for later use.  ...  Messaging is the primary technology for asynchronous process integration (Hohpe and Woolf, 2003).  ...  Environment Council of the Regional Government of Murcia and with funds ERDF of the European Union. 16, 2004.  ... 
doi:10.5220/0001316401510158 fatcat:jm27ggpvlzatzh5t3envzikpbu

Culture and cognition in information technology education

Jaana Holvikivi
2007 European Journal of Engineering Education  
birds and trees") than Finnish students.  ...  According to Mason, certain principles of multiculturalism and respect for others are universal: "This means that we are bound to respect the right of all cultures to live in accordance with their own  ...  trees.. 1 2 3 4 5 This test is intended to determine the way in which you learn.  ... 
doi:10.1080/03043790601055642 fatcat:jywwzsavbzbb5moc7a3uzgk2fe
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