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Complexity of Propositional Proofs under a Promise
[article]
2007
arXiv
pre-print
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We study -- within the framework 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. ...
arXiv:0707.4255v1
fatcat:5iigbvcyw5e5xp7g5z2leb23qa
Complexity of propositional proofs under a promise
2010
ACM Transactions on Computational Logic
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We study -within the framework 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. ...
doi:10.1145/1740582.1740586
fatcat:ehy3fl6bcze3ndcpckgl535dpq
Complexity of Propositional Proofs Under a Promise
[chapter]
Lecture Notes in Computer Science
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We study -within the framework 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. ...
doi:10.1007/978-3-540-73420-8_27
fatcat:3w77gvjfg5aernsvrfc5uorxpq
Characterizing the Existence of Optimal Proof Systems and Complete Sets for Promise Classes
[chapter]
2009
Lecture Notes in Computer Science
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Köbler, Messner, and Torán used the notion 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. ...
doi:10.1007/978-3-642-03351-3_7
fatcat:kz6xzict7zaltgrhfgkjtwydci
On the Existence of Complete Disjoint NP-Pairs
2009
2009 11th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
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Disjoint NP-pairs are an interesting model 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. ...
doi:10.1109/synasc.2009.9
dblp:conf/synasc/Beyersdorff09
fatcat:tpujekk3uvgytiwd4q6ekudd5i
Robust Simulations and Significant Separations
[article]
2010
arXiv
pre-print
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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). ...
arXiv:1012.2034v1
fatcat:vfwmhda34ncfjgxzica7wcxd3q
Robust simulations and significant separations
2017
Information and Computation
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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. ...
doi:10.1016/j.ic.2017.07.002
fatcat:q737uj4vojfiros42l6fjjlebm
Robust Simulations and Significant Separations
[chapter]
2011
Lecture Notes in Computer Science
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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. ...
doi:10.1007/978-3-642-22006-7_48
fatcat:okkkx5sudrb5xc34fsf3uf5v44
Manipulating statistical difference
[chapter]
1998
DIMACS Series in Discrete Mathematics and Theoretical Computer Science
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Preliminary versions 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. ...
doi:10.1090/dimacs/043/14
dblp:conf/dimacs/SahaiV97
fatcat:a2fct6e4mrbz3cpaqinrmg64ja
On complexity of regular realizability problems
[article]
2012
arXiv
pre-print
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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. ...
arXiv:1211.0606v2
fatcat:yhxjuswpyngprhvr4jt3lqc3t4
Probabilistic Parameterized Polynomial Time
[article]
2018
arXiv
pre-print
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This result is accompanied by 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. ...
arXiv:1811.01651v1
fatcat:x6o5ee4qgzd3hhhkqiuce76a5a
Cohesiveness in promise problems
2013
RAIRO - Theoretical Informatics and Applications
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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). ...
doi:10.1051/ita/2013042
fatcat:ymmvzt76brdzpgr7w3lkwmf6ze
Quantum Parameterized Complexity
[article]
2022
arXiv
pre-print
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Parameterized 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. ...
arXiv:2203.08002v1
fatcat:xxd5cwspazfsdlipvhe25ngchy
Different Approaches to Proof Systems
[chapter]
2010
Lecture Notes in Computer Science
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Another approach is to provide 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. ...
doi:10.1007/978-3-642-13562-0_6
fatcat:5hpjwtndsffhtb2uzsoazf6xhm
Fixed-Template Promise Model Checking Problems
[article]
2022
arXiv
pre-print
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We study 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. ...
arXiv:2205.04787v1
fatcat:rb5mpaft3nb2ba6pf2ahd4zvk4
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