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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.  ... 

Computational Complexity of Discrete Problems (Dagstuhl Seminar 17121)

Anna Gál, Michal Koucký, Oded Regev, Till Tantau, Marc Herbstritt
2017 Dagstuhl Reports  
This report documents the program 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.  ... 
doi:10.4230/dagrep.7.3.45 dblp:journals/dagstuhl-reports/GalK0T17 fatcat:og5bioyq4zaszfljjecwfrpjgq

QUANTUM KOLMOGOROV COMPLEXITY AND ITS APPLICATIONS

CATERINA E. MORA, HANS J. BRIEGEL, BARBARA KRAUS
2007 International Journal of Quantum Information  
Furthermore we give some examples of how quantum 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.  ... 
doi:10.1142/s0219749907003171 fatcat:27eptxbcxbblxh7kuybxeffyte

Quantum Kolmogorov complexity and its applications [article]

C. Mora, H. Briegel, B. Kraus
2006 arXiv   pre-print
Furthermore we give some examples of how quantum 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.  ... 
arXiv:quant-ph/0610109v1 fatcat:biwnbxeeqjg4xasx7judowinvq

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.  ... 

Minimum Complexity Pursuit for Universal Compressed Sensing

Shirin Jalali, Arian Maleki, Richard G. Baraniuk
2014 IEEE Transactions on Information Theory  
Towards this end, we use 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).  ... 
doi:10.1109/tit.2014.2302005 fatcat:akmyezmxxfcgja2mb6mmqdkkrq

Minimum Complexity Pursuit for Universal Compressed Sensing [article]

Shirin Jalali, Arian Maleki, Richard Baraniuk
2013 arXiv   pre-print
Using algorithmic information theory tools such as the 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).  ... 
arXiv:1208.5814v2 fatcat:kiufgkpqfjb6fhiasq4nbvug4i

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.  ... 

Information in propositional proofs and algorithmic proof search [article]

Jan Krajicek
2021 arXiv   pre-print
We isolate 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).  ... 
arXiv:2104.04711v3 fatcat:rryraoysnzd75muvi2izsjto3u

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)

Anna Gál, Rahul Santhanam, Till Tantau, Michael Wagner
2019 Dagstuhl Reports  
The following report archives the presentations 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  ... 
doi:10.4230/dagrep.9.3.64 dblp:journals/dagstuhl-reports/GalST19 fatcat:gypvueu2kreclllv3n6eaz6ch4

The Complexity of Complexity [chapter]

Eric Allender
2016 Lecture Notes in Computer Science  
Given a string, what is its 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  ... 
doi:10.1007/978-3-319-50062-1_6 fatcat:6lo4xhsberf4jpuqg7j3kwfg3m

Optimal proof systems for propositional logic and complete sets [chapter]

Jochen Messner, Jacobo Torán
1998 Lecture Notes in Computer Science  
Kraj cek 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  ... 
doi:10.1007/bfb0028583 fatcat:dftglwhnqfbvzprqbdgwd6qtt4

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.  ... 

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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