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Dichotomy Results for Fixed Point Counting in Boolean Dynamical Systems [article]

Christopher M. Homan, Sven Kosub
2008 arXiv   pre-print
We present dichotomy theorems regarding the computational complexity of counting fixed points in boolean (discrete) dynamical systems, i.e., finite discrete dynamical systems over the domain 0,1.  ...  For a class F of boolean functions and a class G of graphs, an (F,G)-system is a boolean dynamical system with local transitions functions lying in F and graphs in G.  ...  Mayr (TU München) for careful proofreading and for pointing out an error in an earlier version of this paper.  ... 
arXiv:0812.0283v1 fatcat:pydc3uatgnc4vkzp4tfx42eequ

DICHOTOMY RESULTS FOR FIXED POINT COUNTING IN BOOLEAN DYNAMICAL SYSTEMS

SVEN KOSUB, CHRISTOPHER M. HOMAN
2007 Theoretical Computer Science  
We present dichotomy theorems regarding the computational complexity of counting fixed points in boolean (discrete) dynamical systems, i.e., finite discrete dynamical systems over the domain {0, 1}.  ...  For a class F of boolean functions and a class G of graphs, an (F, G)-system is a boolean dynamical system with local transitions functions lying in F and graph in G.  ...  We prove dichotomy theorems on the computational complexity of counting fixed points in boolean (discrete) dynamical systems, i.e., finite discrete dynamical systems over the domain {0, 1}.  ... 
doi:10.1142/9789812770998_0018 fatcat:3hcicqah2ncpdfc4e4ykysu6xy

Dichotomy results for fixed point counting in boolean dynamical systems

Christopher M. Homan, Sven Kosub
2015 Theoretical Computer Science  
We present dichotomy theorems regarding the computational complexity of counting fixed points in boolean (discrete) dynamical systems, i.e., finite discrete dynamical systems over the domain {0, 1}.  ...  For a class F of boolean functions and a class G of graphs, an (F, G)-system is a boolean dynamical system with local transitions functions lying in F and graph in G.  ...  We prove dichotomy theorems on the computational complexity of counting fixed points in boolean (discrete) dynamical systems, i.e., finite discrete dynamical systems over the domain {0, 1}.  ... 
doi:10.1016/j.tcs.2015.01.040 fatcat:a37el7y7brg3xdc67ehg7yl3ry

Dichotomy Results for Fixed-Point Existence Problems for Boolean Dynamical Systems [article]

Sven Kosub
2008 arXiv   pre-print
A complete classification of the computational complexity of the fixed-point existence problem for boolean dynamical systems, i.e., finite discrete dynamical systems over the domain 0, 1, is presented.  ...  For function classes F and graph classes G, an (F, G)-system is a boolean dynamical system such that all local transition functions lie in F and the underlying graph lies in G.  ...  Mayr (TU München) for careful proofreading and pointing out an error in earlier versions of this paper.  ... 
arXiv:0801.3802v2 fatcat:c4o6mzrkojdahhz3pp6hlmtkii

Dichotomy Results for Fixed-Point Existence Problems for Boolean Dynamical Systems

Sven Kosub
2008 Mathematics in Computer Science  
A complete classification of the computational complexity of the fixed-point existence problem for boolean dynamical systems, i.e., finite discrete dynamical systems over the domain {0, 1}, is presented  ...  For function classes F and graph classes G, an (F, G)-system is a boolean dynamical system such that all local transition functions lie in F and the underlying graph lies in G.  ...  We characterized the islands of tractability for the fixed-point existence problem for boolean dynamical systems with respect to transition classes F closed under composition and network classes G closed  ... 
doi:10.1007/s11786-007-0038-y fatcat:x2475ebqgvblte6gbf7qcclc7u

The Constraint Satisfaction Problem: Complexity and Approximability (Dagstuhl Seminar 15301)

Andrei A. Bulatov, Venkatesan Guruswami, Andrei Krokhin, Dániel Marx, Marc Herbstritt
2016 Dagstuhl Reports  
This research direction develops at an impressive speed, regularly producing very strong and general results.  ...  The Dagstuhl Seminar 15301 "The Constraint Satisfaction Problem: Complexity and Approximability" was aimed at bringing together researchers using all the different techniques in the study of the CSP, so  ...  The decidability proof is based on results in topological dynamics. Moreover, I showed tight complexity bounds for this problem.  ... 
doi:10.4230/dagrep.5.7.22 dblp:journals/dagstuhl-reports/BulatovGKM15 fatcat:lcyvfsxsbzbrfe27irlpxepxoi

The Complexity of Counting Problems over Incomplete Databases [article]

Marcelo Arenas, Pablo Barceló, Mikaël Monet
2021 arXiv   pre-print
Roughly speaking, we show that counting completions is much harder than counting valuations: for instance, while the latter is always in #P, we prove that the former is not in #P under some widely believed  ...  Specifically, we assume that the domains of these unknown values are finite and, for a Boolean query q, we consider the following two problems: given as input an incomplete database D, (a) return the number  ...  The main conclusion behind our results is that the counting problems studied in this paper are particularly hard from a computational point of view, especially when compared to more positive results obtained  ... 
arXiv:2011.06330v2 fatcat:6uhmm63huvevxbhx2mxvvp6nbq

Computational Counting (Dagstuhl Seminar 18341)

Ivona Bezáková, Leslie Ann Goldberg, Mark R. Jerrum, Marc Herbstritt
2018 Dagstuhl Reports  
A total of 43 researchers from all over the world, with interests and expertise in different aspects of computational counting, actively participated in the meeting.  ...  The seminar was held from 20th to 25th August 2017, at Schloss Dagstuhl -Leibnitz Center for Informatics.  ...  One of the new results, the full dichotomy for Holant c , solves a long-standing open problem.  ... 
doi:10.4230/dagrep.7.8.23 dblp:journals/dagstuhl-reports/BezakovaGJ17 fatcat:yp3oqvgo4fal5lbio5yeqt4uje

Answering Conjunctive Queries under Updates [article]

Christoph Berkholz, Jens Keppeler, Nicole Schweikardt
2017 arXiv   pre-print
For answering Boolean conjunctive queries and for the more general problem of counting the number of solutions of k-ary queries we obtain complete dichotomies: if the query's homomorphic core is q-hierarchical  ...  hardness of dynamic problems.  ...  We obtain the following dichotomies, which are stated from the perspective of data complexity (i.e., the query is regarded to be fixed) and hold for any fixed ε > 0.  ... 
arXiv:1702.06370v1 fatcat:whlmhekt2bf7rdjrf74h7ejezq

Anomalies in the transcriptional regulatory network of the Yeast Saccharomyces cerevisiae

M. Tuğrul, A. Kabakçıoğlu
2010 Journal of Theoretical Biology  
We use a Boolean model of regulatory dynamics with various classes of update functions to represent in vivo regulatory interactions.  ...  An exceptionally large dynamically relevant core network found in Yeast in comparison with the second ensemble points to a strong bias towards a collective organization which is achieved by subtle modifications  ...  Balcan for valuable discussions that led to the present work and a critical reading of the manuscript. We appreciate the help of D. Balcan for providing the model networks at an initial stage.  ... 
doi:10.1016/j.jtbi.2009.12.008 pmid:20004671 fatcat:kqu7uvhwuzegpnadtlf4okgywq

Anomalies in the transcriptional regulatory network of the yeast Saccharomyces cerevisiae [article]

Murat Tugrul, Alkan Kabakcioglu
2009 arXiv   pre-print
We use a Boolean model of regulatory dynamics with various classes of update functions to represent in vivo regulatory interactions.  ...  An exceptionally large dynamically relevant core network found in Yeast in comparison with the second ensemble points to a strong bias towards a collective organization which is achieved by subtle modifications  ...  Balcan for valuable discussions that led to the present work and a critical reading of the manuscript. We appreciate the help of D. Balcan for providing the model networks at an initial stage.  ... 
arXiv:0904.1515v3 fatcat:pxrovqayqrdtbfixhvbgplaq2q

Recent Trends in Knowledge Compilation (Dagstuhl Seminar 17381)

Adnan Darwiche, Pierre Marquis, Dan Suciu, Stefan Szeider, Marc Herbstritt
2018 Dagstuhl Reports  
This report documents the program and the outcomes of Dagstuhl Seminar 17381 "Recent Trends in Knowledge Compilation".  ...  Let f be a Boolean function and let us fix some order of its n variables.  ...  Moreover, I instantiate the dichotomy for the Boolean domain and discuss possible extensions. This is unpublished, ongoing work.  ... 
doi:10.4230/dagrep.7.9.62 dblp:journals/dagstuhl-reports/DarwicheMSS17 fatcat:gitzmlyoxjaapcyjhtpsaqxs3e

Exact Model Counting of Query Expressions

Paul Beame, Jerry Li, Sudeepa Roy, Dan Suciu
2017 ACM Transactions on Database Systems  
There are two main approaches to this problem: (1) in grounded inference one first obtains the lineage for the query and database instance as a Boolean formula, then performs weighted model counting on  ...  We exhibit a class of queries for which model counting can be done in polynomial time using extensional query evaluation, whereas the algorithms used in state-of-the-art exact model counters on their lineages  ...  Our separation results show that this same dichotomy does not extend to decision-DNNF-based algorithms; is there some other general dichotomy that can be shown for this class of algorithms?  ... 
doi:10.1145/2984632 fatcat:2i3xe72q5rd5bk3lczac76t54q

Dynamical regimes and learning properties of evolved Boolean networks

Stefano Benedettini, Marco Villani, Andrea Roli, Roberto Serra, Mattia Manfroni, Antonio Gagliardi, Carlo Pinciroli, Mauro Birattari
2013 Neurocomputing  
Boolean networks (BNs) have been mainly considered as genetic regulatory network models and are the subject of notable works in complex systems biology literature.  ...  The former is an example of the problems in which a dynamical system has to be designed such that its dynamics satisfies given requirements. The latter one is a representative task in classification.  ...  The second issue consists in making the target state a fixed point for the BN.  ... 
doi:10.1016/j.neucom.2012.05.023 fatcat:w3mqka3d3jexxel4rji57sd3su

Coexistence of Dynamics for Two-Dimensional Cellular Automata

Ricardo Severino, Maria Joana Soares, Maria Emilia Athayde
2016 Complex Systems  
Some results obtained for the onedimensional CAs with four peripheral neighbors are also reported, to support our claim that with periodic boundary conditions, the coexistence of dynamics can only appear  ...  Complex Systems, 25  ...  We would like to thank the anonymous referee for many valuable suggestions.  ... 
doi:10.25088/complexsystems.25.1.1 fatcat:4uwii7i2m5bsrcfkkkcruahtxq
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