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Alternation-Trading Proofs, Linear Programming, and Lower Bounds [article]

Ryan Williams
2010 arXiv   pre-print
The proofs of these lower bounds follow a certain proof-by-contradiction strategy that we call alternation-trading. An important open problem is to determine how powerful such proofs can possibly be.  ...  We prove that the search for better lower bounds can often be turned into a problem of solving a large series of linear programming instances.  ...  Thanks to Scott Aaronson for useful discussions about irrelativization, and thanks to the STACS referees for very thoughtful comments.  ... 
arXiv:1001.0746v3 fatcat:2fk6ikn3nncfvoze4wqoqotkx4

Alternation-Trading Proofs, Linear Programming, and Lower Bounds

Ryan Williams
2013 ACM Transactions on Computation Theory  
The size lower bound can be slightly strengthened to quasi-polynomials and other less natural functions.  ...  The algorithms combine known properties of ACC with fast rectangular matrix multiplication and dynamic programming, while the second step requires a strengthening of the author's prior work.  ...  I especially thank Andreas for suggesting the zeta transform as an alternative proof for Lemma 4.2.  ... 
doi:10.1145/2493246.2493249 fatcat:ejhk5koejjfqnfdcn6j7dan7e4

Cumulative subject index volumes 64–67

1985 Information and Control  
138 parallel computational, lower time bounds for solving linear Diophantine equations on, 67, 195 time, see Time models Polygons simple, fast triangulation: algorithm con- struction and applications  ...  : lower time bounds for testing solvability, 67, 195 Equivalence problems computational complexity, for com- mutative grammars, 66, 103 and correctness formulas, for simple loop programs, 65, 18  ... 
doi:10.1016/s0019-9958(85)80038-3 fatcat:cnfpoerj4bgahkwbjf5nrkty5e

Page 3193 of Mathematical Reviews Vol. , Issue 88f [page]

1988 Mathematical Reviews  
For one-time-only branching programs we prove for k-clique func- tions large polynomial lower bounds if k is fixed, and exponential lower bounds for k increasing with n.  ...  Summary: “Branching program depth and the logarithm of branch- ing program complexity are lower bounds on time and space re- quirements for any reasonable model of sequential computation.  ... 

The Pareto Frontier for Random Mechanisms

Timo Mennle, Sven Seuken
2016 Proceedings of the 2016 ACM Conference on Economics and Computation - EC '16  
To illustrate its shape, we apply our results for two different desiderata, namely Plurality and Veto scoring, in settings with 3 alternatives and up to 18 agents. comments on this work.  ...  We study the trade-offs between strategyproofness and other desiderata, such as efficiency or fairness, that often arise in the design of random ordinal mechanisms.  ...  Alternatively, we can incorporate the property as additional constraints in the linear program FindOpt directly.  ... 
doi:10.1145/2940716.2940786 dblp:conf/sigecom/MennleS16 fatcat:y7miwgfrrvfpffbe6a4qgfcfkq

Time-space lower bounds for satisfiability

Lance Fortnow, Richard Lipton, Dieter van Melkebeek, Anastasios Viglas
2005 Journal of the ACM  
Our lower bounds apply to nondeterministic linear time and almost all natural NP-complete problems known.  ...  In fact, they even apply to the class of languages that can be solved on a nondeterministic machine in linear time and space n 1/c . Our proofs follow the paradigm of indirect diagonalization.  ...  Acknowledgments DvM would like to thank Rahul Santhanam, Madhu Sudan, and Iannis Tourlakis for discussions about the topic of this paper and/or comments on earlier drafts.  ... 
doi:10.1145/1101821.1101822 fatcat:thy577mqmne6xcpufkwvhqi7ee

Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs

László Babai, Noam Nisant, Márió Szegedy
1992 Journal of computer and system sciences (Print)  
We also give a new length-width trade-off for oblivious branching programs; in particular, our bound implies new lower bounds on the size of arbitrary branching programs, or on the size of Boolean formulas  ...  We give a tight time-space trade-off of the form TS = @(n'), for general, k-head Turing machines; the bounds hold for a function that can be computed in linear time and constant space by a k + l-head Turing  ...  This time-space trade-off implies some new lower bounds for general branching program size and for Boolean formula size.  ... 
doi:10.1016/0022-0000(92)90047-m fatcat:e4mxtxumwjhh3btjtgng2itrdy

The Pareto Frontier for Random Mechanisms [article]

Timo Mennle, Sven Seuken
2017 arXiv   pre-print
To illustrate its shape, we apply our results for two different desiderata, namely Plurality and Veto scoring, in settings with 3 alternatives and up to 18 agents.  ...  We study the trade-offs between strategyproofness and other desiderata, such as efficiency or fairness, that often arise in the design of random ordinal mechanisms.  ...  Alternatively, we can incorporate the property as additional constraints in the linear program FindOpt directly.  ... 
arXiv:1502.05883v3 fatcat:fzm3kd2ee5e7tpzqouuzxz7p4m

Page 7335 of Mathematical Reviews Vol. , Issue 2000j [page]

2000 Mathematical Reviews  
The lower bound is contrasted by a surprising linear up- per bound for monotone span programs for a function that needs monotone circuit size n®!  ...  Span programs are a linear algebraic model for computing Boolean functions. In the paper first superpolynomial lower bounds are ob- tained for monotone span programs computing explicit functions.  ... 

Effective securities in arbitrage-free markets with bid–ask spreads at liquidation: a linear programming characterization

Mariagiovanna Baccara, Anna Battauz, Fulvio Ortu
2006 Journal of Economic Dynamics and Control  
Although the minimum-cost super-replication problem is non-linear, we introduce an auxiliary problem that allows us to characterize no-arbitrage via linear programming techniques.  ...  We introduce the notion of effective new security and show that effectiveness restricts the no-arbitrage bid and ask prices of a new security to the interval defined by the minimum-cost problem.  ...  Second, we supply a linear programming-based proof of the fact that no-arbitrage per se imposes only an upper bound on the bid and a lower bound on the ask price of a new security.  ... 
doi:10.1016/j.jedc.2004.11.003 fatcat:ybxpqazptfafnimlmhqtmqntdm

Time–Space Tradeoffs for Satisfiability

Lance Fortnow
2000 Journal of computer and system sciences (Print)  
In particular, SAT cannot be solved deterministically by a Turing machine using quasilinear time and √ n space. We also give lower bounds for log-space uniform NC 1 circuits and branching programs.  ...  We combine this work with a result of Nepomnjaščiȋ that shows that a nondeterministic computation of super linear time and sublinear space can be simulated in alternating linear time.  ...  The author thanks Harry Buhrman for many initial discussions on this paper and for allowing the inclusion of Theorem 5.1 and its proof in this paper.  ... 
doi:10.1006/jcss.1999.1671 fatcat:aqeiscdnyfacjjoh26gjhl55ym

Page 497 of The Journal of the Operational Research Society Vol. 60, Issue 4 [page]

2009 The Journal of the Operational Research Society  
The system allowed for the specifica- tions of lower and upper trade-off bounds to support decision- makers (DMs).  ...  the trade-off weights between criteria (Dias and Climaco, 2005).  ... 

Formally Verifying Dynamic Properties of Knowledge Based Systems [chapter]

Perry Groot, Annette ten Teije, Frank van Harmelen
1999 Lecture Notes in Computer Science  
We have used the KIV interactive theorem prover to obtain machine-assisted proofs for all the properties and theorems in this paper.  ...  We present a case-study of a simple classification method for which we formulate and verify two dynamic properties which are concerned with the anytime behaviour and the computation trace of the classification  ...  Thus, the trade-off is between ease of use and flexibility. Non-terminating programs.  ... 
doi:10.1007/3-540-48775-1_10 fatcat:qxjsiqiiljaidp5p26r2kanqca

On the complexity of bilinear forms

Noam Nisan, Avi Wigderson
1995 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing - STOC '95  
This paper provides some new lower and upper bounds on computing bilinear forms by arithmetic circuits. The complexity measures considered are circuit size, formula size and time-space trade-offs.  ...  Acknowledgements We are greatful to Allan Borodin for motivating us to look at time-space trade-off question, as well as for many illuminating converstions.  ...  We conclude this section with a weak lower bound on time-space trade-offs. While weak, note that it implies that linear time algorithms require linear space.  ... 
doi:10.1145/225058.225290 dblp:conf/stoc/NisanW95 fatcat:vrnb35wfs5bypihomndgxiegea

Page 684 of Mathematical Reviews Vol. , Issue 2004a [page]

2004 Mathematical Reviews  
The interconnections among the linear programming formulation, Walrasian equilibrium, and the core are established.  ...  We also present upper and lower bounds on the probabilities of majority preference relations in the population given a sample, using Bayesian updating.  ... 
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