The Parameterized Complexity of Constraint Satisfaction and Reasoning

2013 ◽  
pp. 27-37
Author(s):  
Stefan Szeider
Keyword(s):  
Constraint Satisfaction ◽  
Parameterized Complexity

Parameterized complexity of abduction in Schaefer’s framework

2020 ◽  
Author(s):  
Yasir Mahmood ◽  
Arne Meier ◽  
Johannes Schmidt
Keyword(s):  
Constraint Satisfaction ◽  
Parameterized Complexity ◽  
Algebraic Approach ◽  
Abductive Reasoning ◽  
Fine Grained ◽  
Theory Of Computing ◽  
Reasoning Problem ◽  
Dimensional Classification ◽  
Complexity Classification

Abstract Abductive reasoning is a non-monotonic formalism stemming from the work of Peirce. It describes the process of deriving the most plausible explanations of known facts. Considering the positive version, asking for sets of variables as explanations, we study, besides the problem of wether there exists a set of explanations, two explanation size limited variants of this reasoning problem (less than or equal to, and equal to a given size bound). In this paper, we present a thorough two-dimensional classification of these problems: the first dimension is regarding the parameterized complexity under a wealth of different parameterizations, and the second dimension spans through all possible Boolean fragments of these problems in Schaefer’s constraint satisfaction framework with co-clones (T. J. Schaefer. The complexity of satisfiability problems. In Proceedings of the 10th Annual ACM Symposium on Theory of Computing, May 1–3, 1978, San Diego, California, USA, R.J. Lipton, W.A. Burkhard, W.J. Savitch, E.P. Friedman, A.V. Aho eds, pp. 216–226. ACM, 1978). Thereby, we almost complete the parameterized complexity classification program initiated by Fellows et al. (The parameterized complexity of abduction. In Proceedings of the Twenty-Sixth AAAI Conference on Articial Intelligence, July 22–26, 2012, Toronto, Ontario, Canada, J. Homann, B. Selman eds. AAAI Press, 2012), partially building on the results by Nordh and Zanuttini (What makes propositional abduction tractable. Artificial Intelligence, 172, 1245–1284, 2008). In this process, we outline a fine-grained analysis of the inherent parameterized intractability of these problems and pinpoint their FPT parts. As the standard algebraic approach is not applicable to our problems, we develop an alternative method that makes the algebraic tools partially available again.

scholarly journals Sandwiches for promise constraint satisfaction

2021 ◽  
Vol 82 (1) ◽  
Author(s):  
Guofeng Deng ◽  
Ezzeddine El Sai ◽  
Trevor Manders ◽  
Peter Mayr ◽  
Poramate Nakkirt ◽  
...  
Keyword(s):  
Constraint Satisfaction

On the Parameterized Complexity of Finding Small Unsatisfiable Subsets of CNF Formulas and CSP Instances

2017 ◽  
Vol 18 (3) ◽  
pp. 1-46
Author(s):  
Ronald De Haan ◽  
Iyad Kanj ◽  
Stefan Szeider
Keyword(s):  
Parameterized Complexity ◽  
Cnf Formulas

Parameterized complexity of fair feedback vertex set problem

2021 ◽  
Vol 867 ◽  
pp. 1-12
Author(s):  
Lawqueen Kanesh ◽  
Soumen Maity ◽  
Komal Muluk ◽  
Saket Saurabh
Keyword(s):  
Parameterized Complexity ◽  
Feedback Vertex Set ◽  
Vertex Set ◽  
Feedback Vertex Set Problem
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