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On the Complexity of Finding Narrow Proofs
[article]

2012
*
arXiv
*
pre-print

This lower bound is unconditional and does not rely

arXiv:1204.0775v2
fatcat:nuwbzqnmgren5nzlg3s2dx7ihu
*on*any unproven*complexity*theoretic assumptions.*The*lower bound is matched by a trivial upper bound*of*n^O(k). ... This confirms a conjecture by Vardi, who has first raised*the*question for*the**complexity**of**the*resolution width problem. ... Most state-*of*-*the*-art SAT solvers try to*find*resolution refutations.*One*natural*complexity*measure for resolution is*the*length*of*a refutation. ...##
###
On the Complexity of Finding Narrow Proofs

2012
*
2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
*

*the*Boolean ex. ... (k + 1)-pebble game

*on*Γ ⇐⇒ Γ has a width-k resolution refutation (Atserias, Dalmau '08) Γ = {D ∨ E, C ∨ D ∨ E, A ∨ B ∨ C, A ∨ D ∨ E, B ∨ C ∨ D, D} Spoiler wins

*the*Boolean ex. ... Player 1 wins

*on*I ⇐⇒ Spoiler wins

*on*Γ(I)

*The*reduction We reduce

*the*k-pebble KAI-game

*on*I to

*the*Boolean existential (k+2)-pebble game

*on*Γ(I). ...

##
###
The Skitovich–Darmois and Heyde theorems for complex and quaternion random variables
[article]

2020
*
arXiv
*
pre-print

We also study an analogue

arXiv:2001.07748v1
fatcat:gvy75uuodrhmncc4nljbnhm5aa
*of**the*Heyde theorem for*complex*random variables. ... We prove*the*following analogue*of**the*classical Skitovich–Darmois theorem for*complex*random variables. Let α=a+ib be a nonzero*complex*number. Then*the*following statements hold. 1. ...*The**proof**of*Theorem A, given in [14] , is based*on**the*Polya characterization theorem for*complex*Gaussian random variables in*the**narrow*sense (see [11] ). ...##
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Monte-Carlo Proof-Number Search for Computer Go
[chapter]

2007
*
Lecture Notes in Computer Science
*

It enhances

doi:10.1007/978-3-540-75538-8_5
fatcat:dldvxfrxjjcv3dlvvff5upovju
*proof*-number search by adding*the*flexible Monte-Carlo evaluation. We present*the*new algorithm and evaluate it*on*a sub-problem*of*Go,*the*Life-and-Death problem. ... In order to improve*the*efficiency*of**proof*-number search, we introduce a new algorithm, Monte-Carlo*Proof*-Number search. ... Especially, we would like to thank*one**of*them for his constructive criticism which lead to crucial improvements*on**the*implementational work. ...##
###
Conditional equational theories and complete sets of transformations

1990
*
Theoretical Computer Science
*

*The*completeness

*proof*is based

*on*

*the*observation that each refutation with respect to linear paramodulation and reflection can be modelled by

*the*transformations. ... As certam conditions imposed

*on*an equational theory restrict

*the*search space generated by paramoduiation and reflection we can easily refine our transfiiinations -due to

*the*completeness

*proof*-if

*the*...

*The*

*proof*is by transfinite induction

*on*

*the*

*complexity*

*of*

*the*refutation

*of*EPu{CF} with respect to (+ip, +r}. We assume that

*the*result holds for all M < &I'. ...

##
###
Polya's Characterization Theorem for Complex Random Variables

1997
*
Journal of Complexity
*

Moreover, it is proved that this property characterizes

doi:10.1006/jcom.1997.0457
fatcat:eud5meudv5hzdba56sgcc4nmhy
*the*class*of**complex*Gaussian random variables in*the**narrow*sense; no other*complex*random variable enjoys it. ... A*complex*random variable can be Gaussian in either*the**narrow*or*the*wide sense. ... If we want to maintain this property for*the**complex*case we have to adopt*the**narrow*definition.*The**proof**of*this fact is easy and we give it here for completeness. ...##
###
Many Maybes Mean (Mostly) the Same Thing
[chapter]

2004
*
Studies in Fuzziness and Soft Computing
*

Based

doi:10.1007/978-3-540-44405-3_5
fatcat:ji7skhqfejfdxmu524v6jbqxey
*on*a literature review and a newly developed mathematics*of*"reachability", it is argued that searches through a space containing uncertainties, most*of**the*reachable conclusions will be reached ... via a small number*of*"master variables" in a "*narrow*funnel". ... Acknowledgements*The*arguments in this chapter benefitted greatly from numerous lively discussions with Helen Burgess and Steve Easterbrook. ...##
###
The Ackermann Award 2009
[chapter]

2009
*
Lecture Notes in Computer Science
*

*The*

*proof*-search heuristic in this algorithm is represented by

*the*choice

*of*

*the*branching literal, and, abstracting from

*the*issue

*of*

*finding*

*the*best heuristics, we arrive at

*the*

*proof*system that is ...

*On*

*the*theoretical side, propositional resolution had been considered in

*Proof*

*Complexity*(Tseitin 1968) well before

*the*formal inauguration

*of*

*the*subject (Cook 1975) . ...

##
###
The asymptotics of optimal (equiripple) filters

1999
*
IEEE Transactions on Signal Processing
*

In

doi:10.1109/78.752606
fatcat:zplzgogyhje4tlyy22qltffs5a
*the*transition band,*the*filter response is discovered to be asymptotically close to a scaled error function.*The*main tools are potential theory in*the**complex*plane and asymptotic analysis. ... For equiripple filters,*the*relation among*the*filter length N + 1,*the*transition bandwidth 1!, and*the*optimal passband and stopband errors p and s has been a secret for more than 20 years. ... ACKNOWLEDGMENT*The*authors would like to thank J. Kaiser and A. Oppenheim for their interest in this problem. ...##
###
The Interaction Between Public and Private Enforcement of EU Competition Law: a Case Study of the Swedish Booking Cases

2020
*
Yearbook of Antitrust and Regulatory Studies
*

*The*focus

*of*this article is placed

*on*

*the*assessment carried out by

*the*Swedish courts to determine whether

*the*MFN clauses were restrictive

*of*competition by effect and

*on*

*the*standard

*of*

*proof*attached ... Booking is viewed as an illustration

*of*

*the*increased

*complexity*

*of*competition policy, in particular were novel practices are at issue ... With regard to

*the*standard

*of*

*proof*required by Swedish courts, there is

*on*

*the*

*one*hand a tradition

*of*defining specific standards

*of*

*proof*. ...

##
###
On the numerical radius of operators in Lebesgue spaces
[article]

2010
*
arXiv
*
pre-print

We also give lower bounds for

arXiv:1011.4785v1
fatcat:saxqbps3cbb3doyqvgqqnz25za
*the*best constant*of*equivalence between*the*numerical radius and*the*operator norm in L_p(μ) for atomless μ when restricting to rank-*one*operators or*narrow*operators. ... In other words, we prove that {∫ |x|^p-1|Tx| dμ : x∈ L_p(μ), x_p=1} ≥ p^-1/p q^-1/q T for every T∈L(L_p(μ)) and that this inequality is*the*best possible when*the*dimension*of*L_p(μ) is greater than*one*... Acknowledgments:*The*authors would like to thank Rafael Payá and Beata Randrianantoanina for fruitful conversations concerning*the*matter*of*this paper. ...##
###
A note on propositional proof complexity of some Ramsey-type statements

2010
*
Archive for Mathematical Logic
*

As a consequence

doi:10.1007/s00153-010-0212-9
fatcat:nmlgic2oe5d6reuifbgyrpblli
*of*Pudlák's work in bounded arithmetic [19] it is known that there are quasi-polynomial size constant depth Frege*proofs**of*RAM(4 k , k), but*the**proof**complexity**of*these formulas in ... In this paper we continue*the*study*of*propositional*complexity**of*Ramsey theorem, motivated by*the*following problem: * ... Acknowledgements: I am indebted to Stefan Dantchev (Durham) and Neil Thapen (Prague) for comments*on**the*draft*of**the*paper. ...##
###
Encoding and decoding of BCH codes using light and short codewords

1988
*
IEEE Transactions on Information Theory
*

For high-rate primitive BCH codes this is faster than

doi:10.1109/18.6045
fatcat:cwejcdjuq5hltbvgqzr6fgqcgq
*the*commonly used algorithms, which are nonlinear in n when run*on*sequential machines. ... It is shown that every q-ary primitive BCH code*of*designed distance δ and sufficiently large length n contains a codeword c 0*of*weight w = O(δ ), and degree deg(c 0 ) = o(n). ...*The*technique used is similar to*one*proposed by Kaminski [3] for*finding**the*remainder*of*a long polynomial (or integer) divided by a short*one*. ...##
###
Higher-Order Proof Construction Based on First-Order Narrowing

2008
*
Electronical Notes in Theoretical Computer Science
*

We present

doi:10.1016/j.entcs.2007.09.018
fatcat:6bjlu5dhufgvxoz2wdc2taorci
*the*idea*of*using a*proof*checking algorithm for*the*purpose*of*automated*proof*construction. ... This is achieved by applying*narrowing*search*on*a*proof*checker expressed in a functional programming language. ... (App B [])))) (El (App B []) )))))))) In order to*find*a term*of*this type using*the*proposed approach we should apply*narrowing**on**the*expression tc empctx goalt ? ...##
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Digital fingerprinting codes: problem statements, constructions, identification of traitors

2003
*
IEEE Transactions on Information Theory
*

*The*construction

*complexity*

*of*codes is polynomial in . ... We also present versions

*of*these constructions that afford identification algorithms

*of*

*complexity*( ) = ( ), improving over

*the*best previously known

*complexity*

*of*( ). ... A notable exception is work

*on*tracing traitors [6] , [7] which discusses identification

*complexity*for

*the*

*narrow*-case fingerprinting problem. ...

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