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On some tractable classes in deduction and abduction

2000
*
Artificial Intelligence
*

We map

doi:10.1016/s0004-3702(99)00088-0
fatcat:zare6huitvbu5e2oosbvc5tcka
*tractable**satisfiability*classes to*tractable*entailment classes, including*hierarchies**of**tractable**problems*; and show that some initially promising conditions for*tractability**of*entailment, proposed ... We then consider*a*potential application*of**tractable*entailment, through*a*reduction due to Esghi (1993)*of*certain abduction*problems*to*a*sequence*of*entailment*problems*. ... We provide, first,*a*general connection between*tractable*entailment and*tractable**satisfiability*, which yields*hierarchies**of*classes*of**problems*with*tractable*entailment. ...##
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The Parameterized Complexity of Constraint Satisfaction and Reasoning
[chapter]

2013
*
Lecture Notes in Computer Science
*

Parameterized Complexity is

doi:10.1007/978-3-642-41524-1_2
fatcat:ee2md36scbckvne73x7qfkw5ra
*a*new and increasingly popular theoretical framework for the rigorous analysis*of*NP-hard*problems*and the development*of*algorithms for their solution. ... The framework provides adequate concepts for taking structural aspects*of**problem*instances into account. ... Take for example the*satisfiability**problem*(Sat)*of*propositional reasoning. ...##
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Capturing structure in hard combinatorial problems

2013
*
2013 IEEE 25th International Conference on Tools with Artificial Intelligence
*

SAT is well-suited as

doi:10.1109/ictai.2013.136
dblp:conf/ictai/Szeider13
fatcat:da5r7643mbafrkvaw74evlwbra
*a*target*problem*since by means*of*FPT-reductions to SAT we can make today's extremely powerful SAT solvers applicable to*problems*at higher levels*of*the Polynomial*Hierarchy*. ... number*of**satisfied*clauses beyond*a*guaranteed value [6], the local consistency checking*problem*for constraint networks is naturally parameterized by the level*of*local consistency (k-consistency) [ ... SAT is well-suited as*a*target*problem*since by means*of*FPT-reductions to SAT we can make today's extremely powerful SAT solvers applicable to*problems*at higher levels*of*the Polynomial*Hierarchy*. ...##
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On Parameterized Intractability: Hardness and Completeness

2007
*
Computer journal
*

natural computational

doi:10.1093/comjnl/bxm036
fatcat:wjrw57b5nvbfnfib3uii5tviiq
*problems*. ... We study the theory and techniques developed in the research*of*parameterized intractability, emphasizing on parameterized hardness and completeness that imply (stronger) computational lower bounds for ... 1, it can be shown [47] that the tth level*A*[t]*of*the*A*-*hierarchy*can be characterized by the t-alternating weighted*satisfiability**problem*, which may be viewed as the parameterized version*of*the*satisfiability*...##
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On the structure of parameterized problems in NP
[chapter]

1994
*
Lecture Notes in Computer Science
*

Strong evidence is provided that many NP optimization

doi:10.1007/3-540-57785-8_167
fatcat:6ov7m3jppbfwvbjm2ymt4kduna
*problems*are not fixed-parameter*tractable*and that the fixed-parameter intractability*hierarchy*(the W -*hierarchy*) does not collapse. ... Fixed-parameter intractability*of*optimization*problems*in NP is studied based on computational models with limited nondeterminism. ...*A*typical complete*problem*for the "cap class" W [P ]*of*the*hierarchy*is the Weighted Circuit*Satisfiability**problem*. it is conjectured that the W -*hierarchy*is infinite [?] . ...##
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On the Structure of Parameterized Problems in NP

1995
*
Information and Computation
*

Strong evidence is provided that many NP optimization

doi:10.1006/inco.1995.1156
fatcat:rmuo7ocvy5efzmyfgta4qndl3e
*problems*are not fixed-parameter*tractable*and that the fixed-parameter intractability*hierarchy*(the W -*hierarchy*) does not collapse. ... Fixed-parameter intractability*of*optimization*problems*in NP is studied based on computational models with limited nondeterminism. ...*A*typical complete*problem*for the "cap class" W [P ]*of*the*hierarchy*is the Weighted Circuit*Satisfiability**problem*. it is conjectured that the W -*hierarchy*is infinite [?] . ...##
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On the parameterized complexity of the workflow satisfiability problem

2012
*
Proceedings of the 2012 ACM conference on Computer and communications security - CCS '12
*

We also generalize and extend the types

doi:10.1145/2382196.2382287
dblp:conf/ccs/CramptonGY12
fatcat:pjisortvhzc73afqa7yfvzsf5u
*of*constraints that may be defined in*a*workflow specification and prove that the*satisfiability**problem*remains fixed-parameter*tractable*for such constraints. ...*A*workflow specification is said to be*satisfiable*if there exists an assignment*of*users to workflow steps that*satisfies*all the constraints. ... In Section 5, we discuss*a*number*of*extensions to the workflow*satisfiability**problem*, including generalizations*of*the constraint structure and*of*the*satisfiability**problem*itself. ...##
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On the Gap between the Complexity of SAT and Minimization for Certain Classes of Boolean Formulas

2014
*
International Symposium on Artificial Intelligence and Mathematics
*

It is

dblp:conf/isaim/CepekG14
fatcat:kvypiio3orab7k6jzqpd2vhgka
*a*wellknown fact that the*satisfiability**problem*(SAT) for Boolean formulas in*a*conjunctive normal form (CNF) is NP complete, i.e. Σ1 complete. ...*A*literal is*a*variable or its negation.*A*clause is*a*disjunction*of*literals and hence the value ... The second author gratefully acknowledges the support*of*the Charles University Grant Agency (grant No. 1390213). ...##
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Backdoors into Two Occurrences

2020
*
Journal on Satisfiability, Boolean Modeling and Computation
*

These are the first completeness results in lower levels

doi:10.3233/sat-200125
fatcat:ywyuvpjffzc5rhu65xgfgvunsa
*of*the W-*hierarchy*for any backdoor set*problems*. ... Besides that, it is shown that the*problem**of*finding weak backdoor sets is W[2]-complete, for certain*tractable*cases. ...*of*the paper. ...##
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W-Hardness Under Linear FPT-Reductions: Structural Properties and Further Applications
[chapter]

2005
*
Lecture Notes in Computer Science
*

The notion

doi:10.1007/11533719_98
fatcat:ewojc2i2z5gbllf6ynfulngu2a
*of*linear fpt-reductions has been recently used to derive strong computational lower bounds for well-known NP-hard*problems*. ... Additional complexity lower bounds on important computational*problems*are also established. ... It has been*a*well-known open*problem*in parameterized complexity theory whether the W -*hierarchy**satisfies**a*similar collapsing result. ...##
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On the computational hardness based on linear FPT-reductions

2006
*
Journal of combinatorial optimization
*

Some observations on structural properties

doi:10.1007/s10878-006-7137-6
fatcat:rgj3m626hbdk7n72avrzv5lkue
*of*the standard parameterized*hierarchy*, the W-*hierarchy*, are also presented. 1 In this paper, we always assume that complexity functions are "nice" with both ... The notion*of*linear fpt-reductions has been recently introduced to derive strong computational lower bounds for well-known NP-hard*problems*. ...*A*large number*of*parameterized*problems*have been proved to be hard or complete for various levels in the W -*hierarchy*(Downey and Fellows, 1999) . ...##
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Quantum Parameterized Complexity
[article]

2022
*
arXiv
*
pre-print

This framework exposes

arXiv:2203.08002v1
fatcat:xxd5cwspazfsdlipvhe25ngchy
*a*rich classification*of*the complexity*of*parameterized versions*of*QMA-hard*problems*, demonstrating, for example,*a*clear separation between the Quantum Circuit*Satisfiability*... Parameterized complexity theory was developed in the 1990s to enrich the complexity-theoretic analysis*of**problems*that depend on*a*range*of*parameters. ...*problems*for finite levels*of*the QW*hierarchy*. ...##
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Limits of Preprocessing
[article]

2011
*
arXiv
*
pre-print

We show that, subject to

arXiv:1104.5566v2
fatcat:vullevpcbvgr5jxgw4nz3l4q5m
*a*complexity theoretic assumption, none*of*the considered*problems*can be reduced by polynomial-time preprocessing to*a**problem*kernel whose size is polynomial in*a*structural ... We present*a*first theoretical analysis*of*the power*of*polynomial-time preprocessing for important combinatorial*problems*from various areas in AI. ...*A**problem*is called fixed-parameter*tractable*(FPT) if it can be solved in time f (k)p(n) where f is*a*function*of*the parameter k and p is*a*polynomial*of*the input size n. ...##
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The Parameterized Complexity of Counting Problems

2004
*
SIAM journal on computing (Print)
*

As the basis

doi:10.1137/s0097539703427203
fatcat:auo3obkzebf5rd4ruyxriwdheq
*of*this theory, we introduce*a**hierarchy**of*parameterized counting complexity classes #W[t], for t ≥ 1, that corresponds to Downey and Fellows's W-*hierarchy*[13] and show that*a*few central ... This makes it highly unlikely that any*of*these*problems*is fixed-parameter*tractable*, even though their decision versions are fixed-parameter*tractable*. ... It is believed that W [1] strictly contains the class FPT*of*all fixed-parameter*tractable**problems*and that the W-*hierarchy*is strict. ...##
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Incremental Problems in the Parameterized Complexity Setting

2016
*
Theory of Computing Systems
*

Moreover

doi:10.1007/s00224-016-9729-6
fatcat:b475qneyefhofdwjvn7tdbqqji
*tractability*or intractability is not*a*simple function*of*the problem's static complexity, every level*of*the W-*hierarchy*exhibits complete*problems*with both*tractable*and intractable incrementalizations ... Interestingly, some incremental versions*of*hard*problems*become*tractable*, while others remain hard. ... The apparent*tractability**of*an incremental versions*of**problems*from across the W-*hierarchy*may suggest that incremental versions are typically*tractable*. ...
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