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Characterizing the Existence of Optimal Proof Systems and Complete Sets for Promise Classes [chapter]

Olaf Beyersdorff, Zenon Sadowski
2009 Lecture Notes in Computer Science  
We thank the anonymous referees for helpful comments and detailed suggestions on how to improve this paper.  ...  Our first result characterizes the existence of complete sets for a promise class C by the representability of C in a proof system. Theorem 14.  ...  Optimal Proof Systems and Complete Sets Now we are ready to analyse the relations between our central questions Q1 and Q2 on the existence of optimal proof systems for languages L and the existence of  ... 
doi:10.1007/978-3-642-03351-3_7 fatcat:kz6xzict7zaltgrhfgkjtwydci

Page 10254 of Mathematical Reviews Vol. , Issue 2004m [page]

2004 Mathematical Reviews  
To do this the paper introduces the notion of a test set for a promise class C, and proves that C has a many-one complete set if and only if C has a test set T with a p-optimal proof system. Soren M.  ...  The paper shows that there is a close connection between the existence of optimal proof sys- tems, and the existence of complete problems for certain promise classes like UP, NPM Sparse, RP and BBP.  ... 

Optimal proof systems imply complete sets for promise classes

Johannes Köbler, Jochen Messner, Jacobo Torán
2003 Information and Computation  
For this we introduce the notion of a test set for a promise class C and prove that C has a many-one complete set if and only if C has a test set T with a p-optimal proof system.  ...  In this paper we show a close connection between the existence of (p-)optimal proof systems and the existence of complete problems for certain promise complexity classes like UP, N P ∩ Sparse, RP or BPP  ...  Acknowledgments The authors would like to thank the anonymous referees for very helpful comments.  ... 
doi:10.1016/s0890-5401(03)00058-0 fatcat:qrxbqqamdzhd7kucjc6mlcvtsq

On an optimal propositional proof system and the structure of easy subsets of TAUT

Zenon Sadowski
2002 Theoretical Computer Science  
As a corollary we obtain the result that if there does not exist an optimal propositional proof system, then for every theory T there exists an easy subset of TAUT which is not T -provably easy.  ...  In this paper we develop a connection between optimal propositional proof systems and structural complexity theory-speciÿcally, there exists an optimal propositional proof system if and only if there is  ...  This means that the problem of the existence of complete languages for promise classes and the problem of the existence of optimal proof systems for TAUT , although distant at ÿrst sight, are structurally  ... 
doi:10.1016/s0304-3975(01)00155-4 fatcat:eakmtyjifbdyriqlpdxvzo6cda

On the Existence of Complete Disjoint NP-Pairs

Olaf Beyersdorff
2009 2009 11th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing  
The question whether there exists a complete disjoint NP-pair was posed by Razborov in 1994 and is one of the most important problems in the field.  ...  In addition, we exhibit candidates for complete NP-pairs and apply our results to a recent line of research on the construction of hard tautologies from pseudorandom generators.  ...  ACKNOWLEDGMENTS I thank Jan Krajíček and Zenon Sadowski for helpful discussions on the topic of this paper.  ... 
doi:10.1109/synasc.2009.9 dblp:conf/synasc/Beyersdorff09 fatcat:tpujekk3uvgytiwd4q6ekudd5i

On a P-optimal Proof System for the Set of All Satisfiable Boolean Formulas (SAT) [chapter]

Zenon Sadowski
2001 Lecture Notes in Computer Science  
In this paper we show that the problem of the existence of a p-optimal proof system for SAT can be characterized in a similar manner as J. Hartmanis and L.  ...  Namely, there exists a p-optimal proof system for SAT if and only if there is a suitable recursive presentation of the class of all easy (polynomial time recognizable) subsets of SAT.  ...  If there does not exist a p-optimal proof system for SAT, then for every theory T there exists an easy subset of SAT which is not T-provably easy. Proof.  ... 
doi:10.1007/3-540-45132-3_21 fatcat:23lv3rugt5hhhaktvp7i5blrba

Optimal Proof Systems and Sparse Sets [chapter]

Harry Buhrman, Steve Fenner, Lance Fortnow, Dieter van Melkebeek
2000 Lecture Notes in Computer Science  
Cook and Reckhow also ask about the possibility of whether optimal proof systems exist.  ...  We exhibit a relativized world where NP n SPARSE has no complete sets. This gives the first relativized world where no optimal proof systems exist.  ...  -If p-optimal proof systems exist then UP has complete sets. -If optimal proof systems exist then NP n SPARSE has complete sets.  ... 
doi:10.1007/3-540-46541-3_34 fatcat:iombfkqz3fd5pgazv4tklwclfq

Is the Standard Proof System for SAT P-Optimal? [chapter]

Johannes Köbler, Jochen Messner
2000 Lecture Notes in Computer Science  
A p-optimal proof system for SAT is shown to imply (1) that there exists a complete function for the class of all total nondeterministic multi-valued functions and (2) that any set with an optimal proof  ...  We investigate the question whether there is a (p-)optimal proof system for SAT or for TAUT and its relation to completeness and collapse results for nondeterministic function classes.  ...  The observations from 19, 16, 11] that a p-optimal proof system for a set L implies the existence of a complete set for a certain promise class in fact shows a relationship between di erent completeness  ... 
doi:10.1007/3-540-44450-5_29 fatcat:dzvqiuiz5zehlma4vfnmlhcwsa

Nondeterministic functions and the existence of optimal proof systems

Olaf Beyersdorff, Johannes Köbler, Jochen Messner
2009 Theoretical Computer Science  
Assuming only the existence of a p-optimal proof system for SAT, we show that every set with an optimal proof system has a p-optimal proof system.  ...  We show that Q1 for the class NPMV t is equivalent to the question whether the standard proof system for SAT is p-optimal, and to the assumption that every optimal proof system is p-optimal.  ...  And finally, the existence of optimal proof systems for TAUT and p-optimal proof systems for SAT implies the existence of complete functions for NPSV t (or equivalently, complete sets for NP ∩ coNP).  ... 
doi:10.1016/j.tcs.2009.05.021 fatcat:aaayuozjijai7luet3p5fd36vu

Different Approaches to Proof Systems [chapter]

Olaf Beyersdorff, Sebastian Müller
2010 Lecture Notes in Computer Science  
We remark that optimal proof systems are known to imply complete sets for various promise classes [KMT03] , and this relation also holds in the presence of advice [BS09] .  ...  This question has interesting consequences such as existence of complete languages for promise classes [KMT03, BS09] .  ... 
doi:10.1007/978-3-642-13562-0_6 fatcat:5hpjwtndsffhtb2uzsoazf6xhm

The Deduction Theorem for Strong Propositional Proof Systems [chapter]

Olaf Beyersdorff
2007 Lecture Notes in Computer Science  
We define and investigate different deduction properties and show that the presence of these deduction properties for strong proof systems is powerful enough to characterize the existence of optimal and  ...  In particular, this yields a sufficient condition for the completeness of the canonical pair of Frege systems and provides a general framework for the search for complete NP-pairs.  ...  I also wish to thank Sebastian Müller and the anonymous referees for very helpful suggestions on how to improve this paper.  ... 
doi:10.1007/978-3-540-77050-3_20 fatcat:2b7dlniphnfv3ofvduq62i3tce

The Deduction Theorem for Strong Propositional Proof Systems

Olaf Beyersdorff
2008 Theory of Computing Systems  
We define and investigate different deduction properties and show that the presence of these deduction properties for strong proof systems is powerful enough to characterize the existence of optimal and  ...  In particular, this yields a sufficient condition for the completeness of the canonical pair of Frege systems and provides a general framework for the search for complete NP-pairs.  ...  I also wish to thank Sebastian Müller and the anonymous referees for very helpful suggestions on how to improve this paper.  ... 
doi:10.1007/s00224-008-9146-6 fatcat:tn76ejrx25fp3j6wg4i725v7c4

NP-Completeness, Proof Systems, and Disjoint NP-Pairs

Titus Dose, Christian Glaßer, Markus Bläser, Christophe Paul
2020 Symposium on Theoretical Aspects of Computer Science  
of the set of hard formulas of propositional proof systems.  ...  The article investigates the relation between three well-known hypotheses. - H_{union}: the union of disjoint ≤^p_m-complete sets for NP is ≤^p_m-complete - H_{opps}: there exist optimal propositional  ...  The second one addresses the existence of optimal propositional proof systems.  ... 
doi:10.4230/lipics.stacs.2020.9 dblp:conf/stacs/DoseG20 fatcat:xml37ro4qzc53j6bozg6shoaa4

DeepVentilation: Learning to Predict Physical Effort from Breathing

Sagar Sen, Pierre Bernabé, Erik Johannes B.L.G. Husom
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
The system is used to track physical effort closely matching our perception of actual exercise intensity. The source code for the demo is available here: https://github.com/simula-vias/DeepVentilation  ...  DeepVentilation has been trained on input signals of expansion and contraction of the rib-cage obtained using a non-invasive respiratory inductance plethysmography sensor to predict minute ventilation  ...  Acknowledgments This work was partially supported by JSPS Kakenhi Grant Numbers JP17H04695 and JP20H00587. The author thanks all the co-authors, collaborators, and discussants.  ... 
doi:10.24963/ijcai.2020/730 dblp:conf/ijcai/Todo20 fatcat:w43fsp4qhreozhfgxvrycsha34

QMA variants with polynomially many provers [article]

Sevag Gharibian, Jamie Sikora, Sarvagya Upadhyay
2012 arXiv   pre-print
Using cone programming duality, we give an alternate proof of a result of Harrow and Montanaro [FOCS, pp. 633--642 (2010)] that shows a perfect parallel repetition theorem for SepQMA(m) for any m.  ...  We then study the class BellQMA(poly), characterized by a verifier who first applies unentangled, nonadaptive measurements to each of the polynomially many proofs, followed by an arbitrary but efficient  ...  We also thank the EU-Canada Exchange Program and LI-AFA, Paris for their hospitality, where part of this work was completed. SG acknowledges support from NSERC, NSERC MSFSS, the David R.  ... 
arXiv:1108.0617v2 fatcat:bbcu2jzn2remjpzkqheanoo2qu
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