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Page 4452 of Mathematical Reviews Vol. , Issue 99g
[page]

1999
*
Mathematical Reviews
*

Mariko Yasugi (J-KSUS; Kyoto)
99g:03061 03F20 68Q30 Schoning, Uwe (D-ULM-TI; Ulm)

*Resolution**proofs*,*exponential**bounds*,*and**Kolmogorov**complexity*. ... Summary: “We prove an*exponential*lower*bound*for the length of any*resolution**proof*for the same set of clauses as the one used by A. I. F. Urquhart [J. Assoc. Comput. ...##
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Computational Complexity of Discrete Problems (Dagstuhl Seminar 17121)

2017
*
Dagstuhl Reports
*

This report documents the program

doi:10.4230/dagrep.7.3.45
dblp:journals/dagstuhl-reports/GalK0T17
fatcat:og5bioyq4zaszfljjecwfrpjgq
*and*the outcomes of Dagstuhl Seminar 17121 "Computational*Complexity*of Discrete Problems". ... The first section gives an overview of the topics covered*and*the organization of the meeting. Section 2 lists the talks given in alphabetical order. ...*Proof**complexity**Proof**complexity*aims at separating*complexity*classes by proving lower*bounds*on various*proof*systems. ...##
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QUANTUM KOLMOGOROV COMPLEXITY AND ITS APPLICATIONS

2007
*
International Journal of Quantum Information
*

Furthermore we give some examples of how quantum

doi:10.1142/s0219749907003171
fatcat:27eptxbcxbblxh7kuybxeffyte
*Kolmogorov**complexity*can be applied to prove results in different fields, such as quantum computation*and*thermodynamics,*and*we generalize it to the case ... We show that for any definition of quantum*Kolmogorov**complexity*measuring the number of classical bits required to describe a pure quantum state, there exists a pure n-qubit state which requires*exponentially*... We acknowledge support by the Austrian Science Foundation (FWF), the EU (OLAQUI, SCALA, QICS),*and*the Elise Richter Program. ...##
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Quantum Kolmogorov complexity and its applications
[article]

2006
*
arXiv
*
pre-print

Furthermore we give some examples of how quantum

arXiv:quant-ph/0610109v1
fatcat:biwnbxeeqjg4xasx7judowinvq
*Kolmogorov**complexity*can be applied to prove results in different fields, such as quantum computation*and*thermodynamics,*and*we generalize it to the case ... We show that for any definition of quantum*Kolmogorov**complexity*measuring the number of classical bits required to describe a pure quantum state, there exists a pure n-qubit state which requires*exponentially*... We acknowledge support by the Austrian Science Foundation (FWF), the EU (OLAQUI, SCALA, QICS),*and*the Elise Richter Program. ...##
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Page 4543 of Mathematical Reviews Vol. , Issue 93h
[page]

1993
*
Mathematical Reviews
*

The author concentrates on the comparison of two types of nonuni- form

*complexity*measures (*Kolmogorov**complexity**and*grammar size*complexity*) for the most current classes of formal languages*and*the corresponding ... The Herbrand theorem is shown,*and*the Robinson unification*and**resolution*method is presented, as well as a short introduction to Horn clauses*and*the SLD*resolution*. ...##
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Minimum Complexity Pursuit for Universal Compressed Sensing

2014
*
IEEE Transactions on Information Theory
*

Towards this end, we use

doi:10.1109/tit.2014.2302005
fatcat:akmyezmxxfcgja2mb6mmqdkkrq
*Kolmogorov**complexity*, which is a measure of*complexity*for finite-alphabet sequences introduced by Solomonoff [8]*and**Kolmogorov*[9]. ... Using algorithmic information theory tools such as the*Kolmogorov**complexity*, we provide a unified definition of structure*and*simplicity. ... K [·]m n (x) ≤ κ n m n . (7) Note that κ n m n is an upper*bound*on the*Kolmogorov**complexity*of x o at*resolution*m n . We call this algorithm low-*complexity*least squares (LLS). ...##
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Minimum Complexity Pursuit for Universal Compressed Sensing
[article]

2013
*
arXiv
*
pre-print

Using algorithmic information theory tools such as the

arXiv:1208.5814v2
fatcat:kiufgkpqfjb6fhiasq4nbvug4i
*Kolmogorov**complexity*, we provide a unified definition of structure*and*simplicity. ... to recover a signal of*complexity*\kappa*and*ambient dimension n. ... K [·]m (x) ≤ κ m,n m. (7) Note that κ m,n m is an upper*bound*on the*Kolmogorov**complexity*of x o at*resolution*m. We call this algorithm low-*complexity*least squares (LLS). ...##
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Page 5206 of Mathematical Reviews Vol. , Issue 89I
[page]

1989
*
Mathematical Reviews
*

Equivalently, they are the sets of high self-referential

*Kolmogorov**complexity*. ... Balcdézar (E-UPBI) 891:68044 68Q15 68Q05 Krause, Matthias (DDR-HUMB)*Exponential*lower*bounds*on the*complexity*of local*and*real-time branching programs. (German*and*Russian summaries) J. Inform. ...##
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Information in propositional proofs and algorithmic proof search
[article]

2021
*
arXiv
*
pre-print

We isolate

arXiv:2104.04711v3
fatcat:rryraoysnzd75muvi2izsjto3u
*and*motivate the problem to establish unconditional super-logarithmic lower*bounds*for i_P(τ) where no super-polynomial size lower*bounds*are known. ... We study from the*proof**complexity*perspective the (informal)*proof*search problem: Is there an optimal way to search for propositional*proofs*? ...*Proof*π may have size*exponential*in comparison with the size of the defining circuit. Hence its Kt-*complexity*may be close to the lower*bound*log |π| from (1). ...##
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Page 1746 of Mathematical Reviews Vol. , Issue 95c
[page]

1995
*
Mathematical Reviews
*

circuits with low resource-

*bounded**Kolmogorov**complexity*. ... In recent years exciting progress in the field has been achieved, including the close connection between interactive*proof*systems*and*classical*complexity*classes,*and*the*resolution*of several open problems ...##
###
Computational Complexity of Discrete Problems (Dagstuhl Seminar 19121)

2019
*
Dagstuhl Reports
*

The following report archives the presentations

doi:10.4230/dagrep.9.3.64
dblp:journals/dagstuhl-reports/GalST19
fatcat:gypvueu2kreclllv3n6eaz6ch4
*and*activities of the March 2019 Dagstuhl Seminar 19121 "Computational*Complexity*of Discrete Problems". ... Section 1 summarizes the topics*and*some specific results offered in selected talks during the course of the week. ... We show*exponential*lower*bounds*on*resolution**proof*length for pigeonhole principle (PHP) formulas*and*perfect matching formulas over highly unbalanced, sparse expander graphs, thus answering the challenge ...##
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The Complexity of Complexity
[chapter]

2016
*
Lecture Notes in Computer Science
*

Given a string, what is its

doi:10.1007/978-3-319-50062-1_6
fatcat:6lo4xhsberf4jpuqg7j3kwfg3m
*complexity*? We survey what is known about the computational*complexity*of this problem,*and*describe several open questions. ... of his recent unpublished results),*and*Toni Pitassi (for helpful discussions). ... Acknowledgments The author acknowledges the support of NSF grant CCF-1555409,*and*thanks Diptarka Chakraborty (for helpful comments on an earlier draft of this work), Shuichi Hirahara (for allowing mention ...##
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Optimal proof systems for propositional logic and complete sets
[chapter]

1998
*
Lecture Notes in Computer Science
*

Kraj cek

doi:10.1007/bfb0028583
fatcat:dftglwhnqfbvzprqbdgwd6qtt4
*and*Pudl ak 15, 14] have given a su cient condition for the existence of such optimal systems, showing that if the deterministic*and*nondeterministic*exponential*time classes coincide, then p-optimal ... Cook*and*Reckhow de ned this concept in 6]*and*in order to compare the relative strength of di erent*proof*systems, they considered the notion of p-simulation. ... We show in Section 3 that if the deterministic*and*nondeterministic double*exponential*time*complexity*classes coincide (EE = NEE) then p-optimal*proof*systems exist,*and*that NEE = co-NEE is su cient ...##
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Page 4210 of Mathematical Reviews Vol. , Issue 99f
[page]

1999
*
Mathematical Reviews
*

Comparing instance

*complexity*to*Kolmogorov**complexity*, they stated the ‘instance*complexity*conjecture’, that every set not in P has p-hard instances. ... We give a complete characterization of the class of recursive sets comparing the instance*complexity*to a relativized*Kolmogorov**complexity*of strings. ...##
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Page 2742 of Mathematical Reviews Vol. , Issue 99d
[page]

1991
*
Mathematical Reviews
*

Uwe Schéning,

*Resolution**proofs*,*exponential**bounds*,*and**Kolmogorov**complexity*(110-116); Foto Afrati, Irene Guessarian*and*Michel de Rougemont, The expressiveness of Datalog circuits (DAC) (119-128); ... Kazuo Iwama,*Complexity*of finding short*resolution**proofs*(309-318); S. Jukna, A. Razborov [A. A. Razborov], P. Savicky*and*I. ...
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