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Complexity of Propositional Proofs under a Promise
[article]

2007
*
arXiv
*
pre-print

We study -- within the framework

arXiv:0707.4255v1
fatcat:5iigbvcyw5e5xp7g5z2leb23qa
*of**propositional**proof**complexity*-- the problem*of*certifying unsatisfiability*of*CNF formulas*under*the*promise*that any satisfiable formula has many satisfying assignments ... To this end, we develop*propositional**proof*systems*under*different measures*of**promises*(that is, different ) as extensions*of*resolution. ... We wish to thank Jan Krajíček for commenting on an early version*of*this paper and Eli Ben-Sasson and Amnon Ta-Shma for useful correspondence and conversations. ...##
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Complexity of propositional proofs under a promise

2010
*
ACM Transactions on Computational Logic
*

We study -within the framework

doi:10.1145/1740582.1740586
fatcat:ehy3fl6bcze3ndcpckgl535dpq
*of**propositional**proof**complexity*-the problem*of*certifying unsatisfiability*of*CNF formulas*under*the*promise*that any satisfiable formula has many satisfying assignments ... To this end, we develop*propositional**proof*systems*under*different measures*of**promises*(that is, different Λ) as extensions*of*resolution. ... We also wish to thank Jan Krajíček for commenting on an earlier version*of*this paper and Eli Ben-Sasson and Amnon Ta-Shma for useful correspondence and conversations. ...##
###
Complexity of Propositional Proofs Under a Promise
[chapter]

*
Lecture Notes in Computer Science
*

We study -within the framework

doi:10.1007/978-3-540-73420-8_27
fatcat:3w77gvjfg5aernsvrfc5uorxpq
*of**propositional**proof**complexity*-the problem*of*certifying unsatisfiability*of*CNF formulas*under*the*promise*that any satisfiable formula has many satisfying assignments ... To this end, we develop*propositional**proof*systems*under*different measures*of**promises*(that is, different Λ) as extensions*of*resolution. ... We also wish to thank Jan Krajíček for commenting on an earlier version*of*this paper and Eli Ben-Sasson and Amnon Ta-Shma for useful correspondence and conversations. ...##
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Characterizing the Existence of Optimal Proof Systems and Complete Sets for Promise Classes
[chapter]

2009
*
Lecture Notes in Computer Science
*

Köbler, Messner, and Torán used the notion

doi:10.1007/978-3-642-03351-3_7
fatcat:kz6xzict7zaltgrhfgkjtwydci
*of**a*test set to measure the*complexity**of*the*promise*. ... Let C be*a**promise**complexity*class and let L be*a*language such that C is expressible in L by*a*length-depending*promise*. ...##
###
On the Existence of Complete Disjoint NP-Pairs

2009
*
2009 11th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
*

Disjoint NP-pairs are an interesting model

doi:10.1109/synasc.2009.9
dblp:conf/synasc/Beyersdorff09
fatcat:tpujekk3uvgytiwd4q6ekudd5i
*of*computation with important applications in cryptography and*proof**complexity*. ... 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. ...##
###
Robust Simulations and Significant Separations
[article]

2010
*
arXiv
*
pre-print

*A*language L has

*a*robust simulation in

*a*

*complexity*class C if there is

*a*language in C which agrees with L on arbitrarily large polynomial stretches

*of*input lengths. ... We define and study

*a*new notion

*of*"robust simulations" between

*complexity*classes which is intermediate between the traditional notions

*of*infinitely-often and almost-everywhere, as well as

*a*corresponding ...

*Proof*. Let Q be

*a*

*promise*problem complete for

*Promise*− MAE

*under*linear-time reductions. Assume, for the purpose

*of*contradiction, that

*Promise*− MAEXP ⊆ r.o.SIZE(poly). ...

##
###
Robust simulations and significant separations

2017
*
Information and Computation
*

*A*language L has

*a*robust simulation in

*a*

*complexity*class C if there is

*a*language in C which agrees with L on arbitrarily large polynomial stretches

*of*input lengths. ... We define and study

*a*new notion

*of*"robust simulations" between

*complexity*classes which is intermediate between the traditional notions

*of*infinitely-often and almost-everywhere, as well as

*a*corresponding ... In order to deal with

*promise*classes in

*a*general way, we take as fundamental the notion

*of*

*a*

*complexity*measure. ...

##
###
Robust Simulations and Significant Separations
[chapter]

2011
*
Lecture Notes in Computer Science
*

*A*language L has

*a*robust simulation in

*a*

*complexity*class C if there is

*a*language in C which agrees with L on arbitrarily large polynomial stretches

*of*input lengths. ... We define and study

*a*new notion

*of*"robust simulations" between

*complexity*classes which is intermediate between the traditional notions

*of*infinitely-often and almost-everywhere, as well as

*a*corresponding ... In order to deal with

*promise*classes in

*a*general way, we take as fundamental the notion

*of*

*a*

*complexity*measure. ...

##
###
Manipulating statistical difference
[chapter]

1998
*
DIMACS Series in Discrete Mathematics and Theoretical Computer Science
*

Preliminary versions

doi:10.1090/dimacs/043/14
dblp:conf/dimacs/SahaiV97
fatcat:a2fct6e4mrbz3cpaqinrmg64ja
*of*this work appeared as SAHAI,*A*., AND VADHAN, S. P. 1997.*A*complete*promise*problem for statistical zero-knowledge, In ... We present the first complete problem for SZK, the class*of**promise*problems possessing statistical zero-knowledge*proofs*(against an honest verifier). ... We are grateful to our advisor, Shafi Goldwasser, for getting us started on the topic*of*statistical zero knowledge and providing direction and advice throughout our work. ...##
###
On complexity of regular realizability problems
[article]

2012
*
arXiv
*
pre-print

*A*regular realizability (RR) problem is testing nonemptiness

*of*intersection

*of*some fixed language (filter) with given regular language. We study here

*complexity*

*of*RR problems. ... It implies that for any level

*of*polynomial hierarchy there exists complete RR problem

*under*polynomial reductions. ... Any

*promise*problem (L 1 , L 0 ) with L 1 = ∅ is equivalent to RR

*promise*problem

*under*nlog space reductions.

*Proof*. ...

##
###
Probabilistic Parameterized Polynomial Time
[article]

2018
*
arXiv
*
pre-print

This result is accompanied by

arXiv:1811.01651v1
fatcat:x6o5ee4qgzd3hhhkqiuce76a5a
*a*Cook-style*proof**of*completeness for the corresponding*promise*class (*under**a*suitable notion*of*reduction) for parameterized approximation versions*of*the inference problem ... We examine*a*parameterized*complexity*class for randomized computation where only the error bound and not the full runtime is allowed to depend more than polynomially on the parameter, based on*a*proposal ...*Under*the*promise*that Pr(h) ∈ (q − ǫ, q + ǫ), the probability*of*giving the correct answer is now at least 1 2 + ǫ 2 , hence the problem is in pPPPT.*Proposition*4. ...##
###
Cohesiveness in promise problems

2013
*
RAIRO - Theoretical Informatics and Applications
*

*Promise*problems have been introduced in 1985 by S.Even e.a. as

*a*generalization

*of*decision problems. ... Using

*a*very general approach we study solvability and unsolvability conditions for

*promise*problems

*of*set families and languages. ...

*Proposition*2.4. cohesive(F) is closed

*under*finite variation.

*Proof*. Consider

*A*∈ cohesive(F), C ∈ fin(S) and some B ∈ F. Assume that (

*A*∪ C) ∩ B = (

*A*∩ B) ∪ (C ∩ B) / ∈ fin(S). ...

##
###
Quantum Parameterized Complexity
[article]

2022
*
arXiv
*
pre-print

Parameterized

arXiv:2203.08002v1
fatcat:xxd5cwspazfsdlipvhe25ngchy
*complexity*theory was developed in the 1990s to enrich the*complexity*-theoretic analysis*of*problems that depend on*a*range*of*parameters. ... In this paper we establish*a*quantum equivalent*of*classical parameterized*complexity*theory, motivated by the need for new tools for the classifications*of*the*complexity**of*real-world problems. ... We shall now develop the theory*of*QW[P]-completeness. Firstly, we show that QW[P] is closed*under*FPQT reductions.*Proposition*46. QW[P] is closed*under*FPQT reductions.*Proof*. ...##
###
Different Approaches to Proof Systems
[chapter]

2010
*
Lecture Notes in Computer Science
*

Another approach is to provide

doi:10.1007/978-3-642-13562-0_6
fatcat:5hpjwtndsffhtb2uzsoazf6xhm
*a*finer analysis*of**proof*lengths in the model*of*parameterized*proof**complexity*. ... The results show*a*number*of*new phenomena such as the existence*of*optimal*proof*systems with advice or*under*weak oracles. Such results are not known in the classical setting. ...##
###
Fixed-Template Promise Model Checking Problems
[article]

2022
*
arXiv
*
pre-print

We study

arXiv:2205.04787v1
fatcat:rb5mpaft3nb2ba6pf2ahd4zvk4
*a*class*of*problems that generalizes the CSP simultaneously in two directions: we fix*a*set ℒ*of*quantifiers and Boolean connectives, and we specify two versions*of*each constraint, one strong ... We classify the computational*complexity**of*these problems for the existential positive equality-free fragment*of*first-order logic, i.e., ℒ = {∃"}, and we prove some upper and lower bounds for the positive ...*Proposition*19 . 19 Let (*A*, B) be an L-PMC template which is closed*under*complementation. Then L-PMC(*A*, B) is PSPACE-hard.*Proof*. Suppose that (*A*, B) is closed*under*complementation. ...
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