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Complexity of Propositional Proofs under a Promise [article]

Nachum Dershowitz, Iddo Tzameret
2007 arXiv   pre-print
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

Nachum Dershowitz, Iddo Tzameret
2010 ACM Transactions on Computational Logic  
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]

Nachum Dershowitz, Iddo Tzameret
Lecture Notes in Computer Science  
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]

Olaf Beyersdorff, Zenon Sadowski
2009 Lecture Notes in Computer Science  
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

Olaf Beyersdorff
2009 2009 11th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing  
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]

Lance Fortnow, Rahul Santhanam
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).  ... 
arXiv:1012.2034v1 fatcat:vfwmhda34ncfjgxzica7wcxd3q

Robust simulations and significant separations

Lance Fortnow, Rahul Santhanam
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.  ... 
doi:10.1016/j.ic.2017.07.002 fatcat:q737uj4vojfiros42l6fjjlebm

Robust Simulations and Significant Separations [chapter]

Lance Fortnow, Rahul Santhanam
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.  ... 
doi:10.1007/978-3-642-22006-7_48 fatcat:okkkx5sudrb5xc34fsf3uf5v44

Manipulating statistical difference [chapter]

Amit Sahai, Salil Vadhan
1998 DIMACS Series in Discrete Mathematics and Theoretical Computer Science  
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]

Mikhail N. Vyalyi
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.  ... 
arXiv:1211.0606v2 fatcat:yhxjuswpyngprhvr4jt3lqc3t4

Probabilistic Parameterized Polynomial Time [article]

Nils Donselaar
2018 arXiv   pre-print
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

Ulrike Brandt, Hermann K.-G. Walter
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).  ... 
doi:10.1051/ita/2013042 fatcat:ymmvzt76brdzpgr7w3lkwmf6ze

Quantum Parameterized Complexity [article]

Michael J. Bremner, Zhengfeng Ji, Ryan L. Mann, Luke Mathieson, Mauro E.S. Morales, Alexis T.E. Shaw
2022 arXiv   pre-print
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]

Olaf Beyersdorff, Sebastian Müller
2010 Lecture Notes in Computer Science  
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]

Kristina Asimi, Libor Barto, Silvia Butti
2022 arXiv   pre-print
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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