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Resource Trade-offs in Syntactically Multilinear Arithmetic Circuits

Maurice Jansen, Meena Mahajan, B. V. Raghavendra Rao
2013 Computational Complexity  
We then focus on polynomial-size syntactically multilinear circuits, and study relationships between classes of functions obtained by imposing various resource (width, depth, degree) restrictions on these  ...  As a partial answer to this question, we give a construction which shows that syntactically multilinear circuits of constant width and polynomial degree can be depth-reduced, which in our notation shows  ...  Acknowledgements The results in this paper were announced in MFCS 2008 and CSR 2009 , in Jansen & Rao (2009 Mahajan & Rao (2008) .  ... 
doi:10.1007/s00037-013-0072-x fatcat:6jg6o6x5k5bkvm6tazo5dtm4fe

Balancing Bounded Treewidth Circuits [chapter]

Maurice Jansen, Jayalal Sarma M.N.
2010 Lecture Notes in Computer Science  
From this we derive the analogous statement for syntactically multilinear arithmetic circuits, which strengthens a theorem of Mahajan and Rao.  ...  For our main construction, we prove that multiplicatively disjoint arithmetic circuits of size n^O(1) and treewidth k can be simulated by bounded fan-in arithmetic formulas of depth O(k^2 n).  ...  In essense, this asks for a trade-off, trading non-determinism with stack access.  ... 
doi:10.1007/978-3-642-13182-0_21 fatcat:zbid7xnlpzaerac2zromqibccq

Stronger Lower Bounds and Randomness-Hardness Trade-Offs Using Associated Algebraic Complexity Classes

Maurice Jansen, Rahul Santhanam, Marc Herbstritt
2012 Symposium on Theoretical Aspects of Computer Science  
We consider the special case low-PIT of identity testing for (constant-free) arithmetic circuits with low formal degree, and give improved hardness-to-randomness trade-offs that apply to this case.  ...  Namely, we show that low-PIT ∈ i.o-NTIME[2 n o(1) ]/n o(1) if and only if there exists a family of multilinear polynomials in a·NE/lin that requires constant-free arithmetic circuits of super-polynomial  ...  For the special case of low-PIT, we also make progress on trade-offs that go in the opposite direction.  ... 
doi:10.4230/lipics.stacs.2012.519 dblp:conf/stacs/JansenS12 fatcat:qe34yv6bfnekzl2jzrmc7eg5p4

Small Space Analogues of Valiant's Classes and the Limitations of Skew Formulas

Meena Mahajan, B. V. Raghavendra Rao
2011 Computational Complexity  
Looking for a similar relationship in Valiant's algebraic model of computation, we propose width of an arithmetic circuit as a possible measure of space.  ...  In the uniform circuit model of computation, the width of a boolean circuit exactly characterizes the "space" complexity of the computed function.  ...  The results in this paper were announced in FCT 2009 , in Mahajan & Rao (2009 . Much of this work was done when the second author was at The Institute of Mathematical Sciences, Chennai.  ... 
doi:10.1007/s00037-011-0024-2 fatcat:bnro4engmva25nobjrwr2cxvmq

Proof Complexity (Dagstuhl Seminar 18051)

Albert Atserias, Jakob Nordström, Pavel Pudlák, Rahul Santhanam, Michael Wagner
2018 Dagstuhl Reports  
Proof complexity also gives a way of studying subsystems of Peano Arithmetic where the power of mathematical reasoning is restricted, and to quantify how complex different mathematical theorems are measured  ...  The study of proof complexity was initiated in [Cook and Reckhow 1979] as a way to attack the P vs.  ...  This significantly strengthens the space-width trade-offs in [1] , and provides one more example of trade-offs in the "supercritical" regime above worst case recently identified by [2] .  ... 
doi:10.4230/dagrep.8.1.124 dblp:journals/dagstuhl-reports/AtseriasNPS18 fatcat:5ksfbo2ehfhspcbuw4ppcuyaqu

Pebble Games, Proof Complexity, and Time-Space Trade-offs

Jakob Nordstrom, Reinhard Kahle
2013 Logical Methods in Computer Science  
This is a survey of research in proof complexity drawing on results and tools from pebbling, with a focus on proof space lower bounds and trade-offs between proof size and proof space.  ...  Pebbling has proven to be a useful tool for studying resolution-based proof systems when comparing the strength of different subsystems, showing bounds on proof space, and establishing size-space trade-offs  ...  Thanks also go to Paul Beame and Russell Impagliazzo for keeping me posted about the line of work that led to the time-space trade-off results for resolution in the superlinear space regime.  ... 
doi:10.2168/lmcs-9(3:15)2013 fatcat:ctjbelse45bvzpgl3w52xd6bbi

Subject index volumes 1–200

1999 Theoretical Computer Science  
. negation versus complexity -, 262 results, 5 I3 theorem for space and reversal, 632 trade-offs, 3076 area-time -, 493 between update and retrieve transactions, 343 total deterministic macro tree -, 831  ...  3048 time-optimal solution, 410 time-out, 2012 time-precision tradeoff, 492 time-precision tradeoff problem, 492 on on-line probabilistic Turing machines, 492 timers with arbitrary delays, 3610 space trade-offs  ... 
doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm

Information Sciences and Technologies Bulletin of the ACM Slovakia Stiff Systems Analysis IMS service provisioning improvement Support for Creating Robust Plans and Schedules Generalized Multilinear Model for Dimensionality Reduction of Binary Tensors Development of Domain-Specific Languages Based on Generic Syntax and Functional Composition Stiff Systems Analysis

V Šátek, T Kovácik, P Jankovic, J Mažgut, S Chodarev, L Stareèek, Mária Bieliková, Johann, Viliam Geffert, Tomáš Hruška, Robert Lorencz, Karol Matiaško (+9 others)
2012 unpublished
Digital circuits test optimization by multifunctional components 1 12 23 35 47 54 Aim and Scope of the Information Sciences and Technologies Bulletin of the ACM Slovakia ACM Slovakia offers a forum for  ...  Besides that, conferences that meet bulletin's expectations with regard to scientific rigor are invited to consider publishing their papers in the bulletin in form of special issues.  ...  This paper has been elaborated in the framework of the  ... 

On circuit complexity classes and iterated matrix multiplication

Fengming Wang
arithmetic circuits with bounded individual degree can be performed in subexponential time (and even by a uniform family of deterministic constant-depth AC circuits of subexponential size). 2.  ...  ACC_m circuits are circuits consisting of unbounded fan-in AND, OR and MOD_m gates and unary NOT gates, where m is a fixed integer.  ...  Finally, building on his powerful Switching Lemma, Håstad [Hås86] proved the optimal trade-off between size and depth in terms of AC 0 circuits for the PARITY function.  ... 
doi:10.7282/t35d8qvq fatcat:x4ya6lral5exvbnlqpjsnge3re

D2.3 - GDPR-compliant and Privacy-Preserving Analytics for Healthcare Providers

Suite5, SECURA BV, Tampere University
2020 Zenodo  
The deliverable also reports on investigated and analytics techniques used by CSPs and Healthcare Providers in order to secure their infrastructures against cyber threats.  ...  Performance Issues The trade-off between the supported functionalities and performance issues is also discussed.  ...  As the functional encryption schemes they utilise do not support floating point number operations, they made a trade-off in precision for time efficiency.  ... 
doi:10.5281/zenodo.4022329 fatcat:sdtc5fkkofc6vigeil25ulhm5u

A Decade of Lattice Cryptography

Chris Peikert
2016 Foundations and Trends® in Theoretical Computer Science  
This work surveys most of the major developments in lattice cryptography over the past ten years.  ...  worst-case intractability assumptions, and solutions to long-standing open problems in cryptography.  ...  discrete Gaussian over an appropriate coset c + Z, instead of deterministically. 6 Subsequent works gave other sampling algorithms that offer various trade-offs among efficiency, statistical error, and  ... 
doi:10.1561/0400000074 fatcat:5orjj3lrufdalfufl7ju6rnz3e

Dagstuhl Reports, Volume 8, Issue 9, September 2018, Complete Issue [article]

In this talk, under the more general context of automation in the workplace, we explored how we can identify and map the skills in data science with the capabilities of AI and ML, in order to know when  ...  the analysis in terms of tasks.  ...  Here we provide a depth hierarchy theorem for multilinear arithmetic formulas, where a formula is said to be multilinear if each gate in it computes a multilinear polynomial.  ... 
doi:10.4230/dagrep.8.9 fatcat:5qvmtdru7banpoucejfabfjqdu

Combinatorics and Algorithmics of Strings (Dagstuhl Seminar 14111) Computational Complexity of Discrete Problems (Dagstuhl Seminar 14121) Computational Models of Cultural Behavior for Human-Agent Interaction (Dagstuhl Seminar 14131) Interaction and Collective Movement Processing (Dagstuhl Seminar 14132) Spatial reference in the Semantic Web and in Robotics (Dagstuhl Seminar 14142)

Johannes Fürnkranz, Eyke Hüllermeier, Cynthia Rudin, Scott Sanner, Roman Słowiński, Maxime Crochemore, James Currie, Gregory Kucherov, Dirk Nowotka, Pierre Dillenbourg, Claude Kirchner, John Mitchell (+25 others)
2014 unpublished
Preferences have recently received considerable attention in disciplines such as machine learning, knowledge discovery, information retrieval, statistics, social choice theory, multiple criteria decision  ...  The motivation for this seminar was to showcase recent progress in these different areas with the goal of working towards a common basis of understanding, which should help to facilitate future synergies  ...  We prove that a particular class of ordinary differential equations (ordinary differential equations with polynomial right hand side) can be solved in polynomial time.  ... 

Dagstuhl Reports, Volume 8, Issue 1, January 2018, Complete Issue [article]

Several talks covered the state-of-the-art and work in progress.  ...  It summarized achievements in automated software optimisation.  ...  This significantly strengthens the space-width trade-offs in [1] , and provides one more example of trade-offs in the "supercritical" regime above worst case recently identified by [2] .  ... 
doi:10.4230/dagrep.8.1 fatcat:dv5ntjliznbs7dwohrcmiwr3lm

Coalgebraic Logics (Dagstuhl Seminar 12411) Algebraic and Combinatorial Methods in Computational Complexity (Dagstuhl Seminar 12421) Time-of-Flight Imaging: Algorithms, Sensors and Applications (Dagstuhl Seminar 12431) Foundations and Challenges of Change and Evolution in Ontologies (Dagstuhl Seminar 12441) Requirements Management-Novel Perspectives and Challenges (Dagstuhl Seminar 12442)

Lieven Desmet, Martin Johns, Benjamin Livshits, Andrei Sabelfeld, Ernst-Erich Doberkat, Alexander Kurz, Manindra Agrawal, Thomas Thierauf, Christopher Umans, James Davis, Bernd Jähne, Andreas Kolb (+9 others)
2012 unpublished
We then discuss how computational complexity creeps in and how to cope with it.  ...  In addition, we sketch some approaches for dealing with requirements evolution, adopted from the PhD thesis of Neil Ernst [1].  ...  Prove a structural statement for arithmetic circuits, and 2. find weakness of structure to prove lower bound.  ... 
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