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On some tractable classes in deduction and abduction

Alvaro del Val
2000 Artificial Intelligence  
We map 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.  ... 
doi:10.1016/s0004-3702(99)00088-0 fatcat:zare6huitvbu5e2oosbvc5tcka

The Parameterized Complexity of Constraint Satisfaction and Reasoning [chapter]

Stefan Szeider
2013 Lecture Notes in Computer Science  
Parameterized Complexity is 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.  ... 
doi:10.1007/978-3-642-41524-1_2 fatcat:ee2md36scbckvne73x7qfkw5ra

Capturing structure in hard combinatorial problems

Stefan Szeider
2013 2013 IEEE 25th International Conference on Tools with Artificial Intelligence  
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.  ...  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.  ... 
doi:10.1109/ictai.2013.136 dblp:conf/ictai/Szeider13 fatcat:da5r7643mbafrkvaw74evlwbra

On Parameterized Intractability: Hardness and Completeness

J. Chen, J. Meng
2007 Computer journal  
natural computational 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  ... 
doi:10.1093/comjnl/bxm036 fatcat:wjrw57b5nvbfnfib3uii5tviiq

On the structure of parameterized problems in NP [chapter]

Liming Cai, Jianer Chen, Rodney Downey, Michael Fellows
1994 Lecture Notes in Computer Science  
Strong evidence is provided that many NP optimization 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 [?] .  ... 
doi:10.1007/3-540-57785-8_167 fatcat:6ov7m3jppbfwvbjm2ymt4kduna

On the Structure of Parameterized Problems in NP

L.M. Cai, J. Chen, R. Downey, M. Fellows
1995 Information and Computation  
Strong evidence is provided that many NP optimization 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 [?] .  ... 
doi:10.1006/inco.1995.1156 fatcat:rmuo7ocvy5efzmyfgta4qndl3e

On the parameterized complexity of the workflow satisfiability problem

Jason Crampton, Gregory Gutin, Anders Yeo
2012 Proceedings of the 2012 ACM conference on Computer and communications security - CCS '12  
We also generalize and extend the types 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.  ... 
doi:10.1145/2382196.2382287 dblp:conf/ccs/CramptonGY12 fatcat:pjisortvhzc73afqa7yfvzsf5u

On the Gap between the Complexity of SAT and Minimization for Certain Classes of Boolean Formulas

Ondrej Cepek, Stefan Gurský
2014 International Symposium on Artificial Intelligence and Mathematics  
It is 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).  ... 
dblp:conf/isaim/CepekG14 fatcat:kvypiio3orab7k6jzqpd2vhgka

Backdoors into Two Occurrences

Jan Johannsen
2020 Journal on Satisfiability, Boolean Modeling and Computation  
These are the first completeness results in lower levels 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.  ... 
doi:10.3233/sat-200125 fatcat:ywyuvpjffzc5rhu65xgfgvunsa

W-Hardness Under Linear FPT-Reductions: Structural Properties and Further Applications [chapter]

Jianer Chen, Xiuzhen Huang, Iyad A. Kanj, Ge Xia
2005 Lecture Notes in Computer Science  
The notion 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.  ... 
doi:10.1007/11533719_98 fatcat:ewojc2i2z5gbllf6ynfulngu2a

On the computational hardness based on linear FPT-reductions

Jianer Chen, Xiuzhen Huang, Iyad A. Kanj, Ge Xia
2006 Journal of combinatorial optimization  
Some observations on structural properties 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) .  ... 
doi:10.1007/s10878-006-7137-6 fatcat:rgj3m626hbdk7n72avrzv5lkue

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
This framework exposes 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.  ... 
arXiv:2203.08002v1 fatcat:xxd5cwspazfsdlipvhe25ngchy

Limits of Preprocessing [article]

Stefan Szeider
2011 arXiv   pre-print
We show that, subject to 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.  ... 
arXiv:1104.5566v2 fatcat:vullevpcbvgr5jxgw4nz3l4q5m

The Parameterized Complexity of Counting Problems

Jörg Flum, Martin Grohe
2004 SIAM journal on computing (Print)  
As the basis 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.  ... 
doi:10.1137/s0097539703427203 fatcat:auo3obkzebf5rd4ruyxriwdheq

Incremental Problems in the Parameterized Complexity Setting

Bernard Mans, Luke Mathieson
2016 Theory of Computing Systems  
Moreover 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.  ... 
doi:10.1007/s00224-016-9729-6 fatcat:b475qneyefhofdwjvn7tdbqqji
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