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Model-checking problems as a basis for parameterized intractability

Jörg Flum, Martin Grohe, Leonid Libkin
2005 Logical Methods in Computer Science  
But there are also classes, for example, the A-hierarchy, that are more naturally characterised in terms of model-checking problems for certain fragments of first-order logic.  ...  We improve their result and then prove a similar correspondence between weighted satisfiability and model-checking problems for the A-hierarchy and the W^*-hierarchy.  ...  We are grateful to Catherine McCartin, Rod Downey, and Mike Fellows for various discussions with both authors on the characterisation of the A-hierarchy by alternating weighted satisfiability problems.  ... 
doi:10.2168/lmcs-1(1:2)2005 fatcat:sffal5ce7na7tolyocw6a3n52m

Parameterized Complexity Results for a Model of Theory of Mind Based on Dynamic Epistemic Logic

Iris van de Pol, Iris van Rooij, Jakub Szymanik
2016 Electronic Proceedings in Theoretical Computer Science  
We show that model checking for DEL is PSPACE-hard, also when restricted to single-pointed models and S5 relations, thereby solving an open problem in the literature.  ...  The model is a special case of DEL model checking.  ...  Acknowledgements We thank the reviewers for their comments.  ... 
doi:10.4204/eptcs.215.18 fatcat:asqoeus4xnejjh7ijuspjh4pna

Valiant-Vazirani Lemmata for Various Logics [article]

Moritz Müller
2008 Electronic colloquium on computational complexity  
We show analogues of a theorem due to Valiant and Vazirani [16] for intractable parameterized complexity classes such as W[P], W[SAT] and the classes of the W-hierarchy as well as those of the A-hierarchy  ...  We do so by proving a general "logical" version of it which may be of independent interest.  ...  I thank Jörg Flum for his advice.  ... 
dblp:journals/eccc/Muller08 fatcat:4j2jik6qmvcqdnifzxlk5dowc4

Parameterized Complexity in Cognitive Modeling: Foundations, Applications and Opportunities

I. van Rooij, T. Wareham
2007 Computer journal  
In this paper, we consider the particular benefits of the parameterized complexity framework for identifying sources of intractability in cognitive models.  ...  a useful constraint on cognitive models.  ...  Schouten school at Eindhoven University of Technology and thanks Michael Fellows and Ulrike Stege for discussions that set the seed for this paper.  ... 
doi:10.1093/comjnl/bxm034 fatcat:p2x6vjt24vbvhn7uh5ifqj4dri

The Computational Complexity of Controller-Environment Co-design Using Library Selection for Distributed Construction [chapter]

Mesam Timmar, Todd Wareham
2019 Advanced Structured Materials  
We also consider two elaborations on this problem. First, we analyze the controllerenvironment co-design problem under a new architecture in which robots have a transient memory.  ...  Second, we give the first definitions of and derive computational complexity results for stigmergy-related parameters for the controller-environment co-design problem. ii Acknowledgements I would like  ...  It rules out the possibility of existence of F P T algorithms for a certain parameter set K of polynomial-time intractable problem A by a parameterized reduction from a known intractable class problem  ... 
doi:10.1007/978-3-030-05816-6_4 fatcat:afzvsvu5bjartiuotrnqqqtcda

Towards fully multivariate algorithmics: Parameter ecology and the deconstruction of computational complexity

Michael R. Fellows, Bart M.P. Jansen, Frances Rosamond
2013 European journal of combinatorics (Print)  
We call for a new type of race in parameterized analysis, with the purpose of uncovering the boundaries of tractability by finding the smallest possible parameterizations which admit FPT-algorithms or  ...  An extensive overview of recent advances on this front is presented for the Vertex Cover problem.  ...  Deconstruction of Intractability For practitioners who have to solve NP -hard problems on a daily basis, it is good to know that there are parameterized approaches to tractability which may help them to  ... 
doi:10.1016/j.ejc.2012.04.008 fatcat:uzjyjuxec5hvlcep3jsf3mcupu

Describing parameterized complexity classes

Jörg Flum, Martin Grohe
2003 Information and Computation  
For every classical complexity class we introduce a parameterized analogue in a natural way. In particular, the analogue of polynomial time is the class of all fixed-parameter tractable problems.  ...  We develop a basic complexity theory for the parameterized analogues of classical complexity classes and give, among other things, complete problems and logical descriptions.  ...  We fix some encoding [·] : → N and parameterize the model-checking problem by [ϕ] . Formally, we let p-MC(D, ) = {(A, [ϕ]) | A ∈ D, ϕ ∈ }.  ... 
doi:10.1016/s0890-5401(03)00161-5 fatcat:flbfb4lnkbcmzkpux24ehf5nkm

Describing Parameterized Complexity Classes [chapter]

Jörg Flum, Martin Grohe
2002 Lecture Notes in Computer Science  
For every classical complexity class we introduce a parameterized analogue in a natural way. In particular, the analogue of polynomial time is the class of all fixed-parameter tractable problems.  ...  We develop a basic complexity theory for the parameterized analogues of classical complexity classes and give, among other things, complete problems and logical descriptions.  ...  We fix some encoding [·] : → N and parameterize the model-checking problem by [ϕ] . Formally, we let p-MC(D, ) = {(A, [ϕ]) | A ∈ D, ϕ ∈ }.  ... 
doi:10.1007/3-540-45841-7_29 fatcat:q745fbznazestcb77nidrg62i4

The Birth and Early Years of Parameterized Complexity [chapter]

Rod Downey
2012 Lecture Notes in Computer Science  
Through the hazy lens of (my) memory, I will try to reconstruct how Mike Fellows and I, together with some co-authors in some cases, came up with the basic papers in parameterized complexity.  ...  Whilst circuits were a nice basis and were likely a good enough basis for an intractability theory, the k-step halting problem was so traditional that it completed the picture of W [1] as a gold standard  ...  The idea was to use QBFSat parameterized as the basis for those combinatorial problems usually found to be P SP ACE-complete. I am not sure that we have a nice treatment of space yet.  ... 
doi:10.1007/978-3-642-30891-8_2 fatcat:iyfaamvdunbh7fqvuqcdnijwx4

Limits of Preprocessing

Stefan Szeider
2011 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
problem parameter of the input, such as induced width or backdoor size.  ...  Our results provide a firm theoretical boundary for the performance of polynomial-time preprocessing algorithms for the considered problems.  ...  A composition algorithm for a parameterized problem P ⊆ Σ * × N is an algorithm that receives as input a sequence (x 1 , k), . . . , (x t , k) ∈ Σ * × N, uses time polyno- mial in t i=1 |x i | + k, and  ... 
doi:10.1609/aaai.v25i1.7816 fatcat:3hhd7szh2jdi7o3brlchxqq3g4

Limits of Preprocessing [article]

Stefan Szeider
2011 arXiv   pre-print
problem parameter of the input, such as induced width or backdoor size.  ...  Our results provide a firm theoretical boundary for the performance of polynomial-time preprocessing algorithms for the considered problems.  ...  Formal Background A parameterized problem P is a subset of Σ * × N for some finite alphabet Σ. For a problem instance (x, k) ∈ Σ * × N we call x the main part and k the parameter.  ... 
arXiv:1104.5566v2 fatcat:vullevpcbvgr5jxgw4nz3l4q5m

On Finding Short Resolution Refutations and Small Unsatisfiable Subsets [chapter]

Michael R. Fellows, Stefan Szeider, Graham Wrightson
2004 Lecture Notes in Computer Science  
We show that both problems are complete for the class W[1], the first level of the W-hierarchy of fixed-parameter intractable problems.  ...  We consider the parameterized problems of whether a given set of clauses can be refuted within k resolution steps, and whether a given set of clauses contains an unsatisfiable subset of size at most k.  ...  Acknowledgments The authors thank the referees for suggestions that helped to improve the presentation of the paper.  ... 
doi:10.1007/978-3-540-28639-4_20 fatcat:2xzwc2sbnjgonjhrukgnucwxai

On finding short resolution refutations and small unsatisfiable subsets

Michael R. Fellows, Stefan Szeider, Graham Wrightson
2006 Theoretical Computer Science  
We show that both problems are complete for the class W[1], the first level of the W-hierarchy of fixed-parameter intractable problems.  ...  We consider the parameterized problems of whether a given set of clauses can be refuted within k resolution steps, and whether a given set of clauses contains an unsatisfiable subset of size at most k.  ...  Acknowledgments The authors thank the referees for suggestions that helped to improve the presentation of the paper.  ... 
doi:10.1016/j.tcs.2005.10.005 fatcat:ncfeoii32bcc7fmlp356njhkxu

Separating sets of strings by finding matching patterns is almost always hard

Giuseppe Lancia, Luke Mathieson, Pablo Moscato
2017 Theoretical Computer Science  
We then perform a detailed parameterized analysis of the problem, separating tractable and intractable variants.  ...  We study the complexity of the problem of searching for a set of patterns that separate two given sets of strings.  ...  We also employ a parameterized version of the Model Checking problem, which takes as input a finite structure and a logical formula and asks the question of whether the structure is a model of the formula  ... 
doi:10.1016/j.tcs.2016.12.018 fatcat:jciozho3inbkfdqqmaynqedhum

Variational Inference for Sparse and Undirected Models [article]

John Ingraham, Debora Marks
2017 arXiv   pre-print
Here, we develop a framework for scalable Bayesian inference of discrete undirected models based on two new methods.  ...  parameterizations.  ...  Acknowledgements We thank David Duvenaud, Finale Doshi-Velez, Miriam Huntley, Chris Sander, and members of the Marks lab for helpful comments and discussions.  ... 
arXiv:1602.03807v2 fatcat:3s6lblnx6zajxoyh4bhmq2jaoq
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