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

2009
*
Lecture Notes in Computer Science
*

We thank

doi:10.1007/978-3-642-03351-3_7
fatcat:kz6xzict7zaltgrhfgkjtwydci
*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*...##
###
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

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. ...

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

2002
*
Theoretical Computer Science
*

As a corollary we obtain

doi:10.1016/s0304-3975(01)00155-4
fatcat:eakmtyjifbdyriqlpdxvzo6cda
*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 ...##
###
On the Existence of Complete Disjoint NP-Pairs

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. ...

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

2001
*
Lecture Notes in Computer Science
*

In this paper we show that

doi:10.1007/3-540-45132-3_21
fatcat:23lv3rugt5hhhaktvp7i5blrba
*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*. ...##
###
Optimal Proof Systems and Sparse Sets
[chapter]

2000
*
Lecture Notes in Computer Science
*

Cook

doi:10.1007/3-540-46541-3_34
fatcat:iombfkqz3fd5pgazv4tklwclfq
*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*. ...##
###
Is the Standard Proof System for SAT P-Optimal?
[chapter]

2000
*
Lecture Notes in Computer Science
*

A p-

doi:10.1007/3-540-44450-5_29
fatcat:dzvqiuiz5zehlma4vfnmlhcwsa
*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*...##
###
Nondeterministic functions and the existence of optimal proof systems

2009
*
Theoretical Computer Science
*

Assuming only

doi:10.1016/j.tcs.2009.05.021
fatcat:aaayuozjijai7luet3p5fd36vu
*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). ...##
###
Different Approaches to Proof Systems
[chapter]

2010
*
Lecture Notes in Computer Science
*

We remark that

doi:10.1007/978-3-642-13562-0_6
fatcat:5hpjwtndsffhtb2uzsoazf6xhm
*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] . ...##
###
The Deduction Theorem for Strong Propositional Proof Systems
[chapter]

2007
*
Lecture Notes in Computer Science
*

We define

doi:10.1007/978-3-540-77050-3_20
fatcat:2b7dlniphnfv3ofvduq62i3tce
*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. ...##
###
The Deduction Theorem for Strong Propositional Proof Systems

2008
*
Theory of Computing Systems
*

We define

doi:10.1007/s00224-008-9146-6
fatcat:tn76ejrx25fp3j6wg4i725v7c4
*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. ...##
###
NP-Completeness, Proof Systems, and Disjoint NP-Pairs

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*. ...

##
###
DeepVentilation: Learning to Predict Physical Effort from Breathing

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. ...

##
###
QMA variants with polynomially many provers
[article]

2012
*
arXiv
*
pre-print

Using cone programming duality, we give an alternate

arXiv:1108.0617v2
fatcat:bbcu2jzn2remjpzkqheanoo2qu
*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. ...
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