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Hausdorffization and polynomial twists

Kevin Pilgrim, Laura DeMarco
2010 Discrete and Continuous Dynamical Systems. Series A  
We study dynamical equivalence relations on the moduli space MP d of complex polynomial dynamical systems.  ...  We also study relations of topological conjugacy and the Branner-Hubbard wringing deformation.  ...  We would like to thank David Dumas, Adam Epstein, and Stefan Wenger for helpful discussions.  ... 
doi:10.3934/dcds.2011.29.1405 fatcat:hft73d3dtfal3cv4fmvokcvg7a

Page 10294 of Mathematical Reviews Vol. , Issue 2004m [page]

2004 Mathematical Reviews  
m +m*) time and O(kn) space. We have implemented the two algorithms in or- der to compare them with algorithms that maintain the transitive closure of an incremental graph without using a path cover.  ...  Our algorithm maintains the transitive clo- sure of a digraph of n vertices and m edges (in the final state) in O(km*) time and O(kn) space, where m* is the number of edges in the resulting transitive  ... 

Transitive Closure of a Union of Dependence Relations for Parameterized Perfectly-Nested Loops [chapter]

Włodzimierz Bielecki, Krzysztof Kraska, Tomasz Klimek
2013 Lecture Notes in Computer Science  
This allows us to effectively extract both fine-and coarse-grained parallelism in loops using techniques based on applying the transitive closure of dependence relations.  ...  This paper presents a new approach for computing the transitive closure of a union of relations describing all the dependences in both uniform and quasi-uniform perfectly-nested parameterized loops.  ...  [10] present ways to calculate transitive closure for this purpose. Feautrier and Gonnord [11] and Ancourt et al.  ... 
doi:10.1007/978-3-642-39958-9_4 fatcat:yhsbahxwwjg5tnat6kkaebkzlq

Model checking and transitive-closure logic [chapter]

Neil Immerman, Moshe Y. Vardi
1997 Lecture Notes in Computer Science  
We give a linear-time algorithm to translate any formula from computation tree logic (CTL or CTL*) into an equivalent expression in a variable-con ned fragment of transitive-closure logic FO(TC).  ...  This means that the space requirements are manageable, the entire computation is parallelizable, and e cient dynamic evaluation is possible.  ...  Acknowledgements: Thanks to Kousha Etessami and Thomas Wilke for helpful comments, corrections, and suggestions.  ... 
doi:10.1007/3-540-63166-6_29 fatcat:pozwqznvtbc5ff7ozncmctv37i

Mantaining Dynamic Matrices for Fully Dynamic Transitive Closure [article]

Camil Demetrescu, Giuseppe F. Italiano
2001 arXiv   pre-print
In this paper we introduce a general framework for casting fully dynamic transitive closure into the problem of reevaluating polynomials over matrices.  ...  With this technique, we improve the best known bounds for fully dynamic transitive closure.  ...  Acknowledgements We are indebted to Garry Sagert and Mikkel Thorup for enlightening discussions, and to Valerie King for many useful comments and insights on this work.  ... 
arXiv:cs/0104001v1 fatcat:brp2hexcxfanvjhqzbh5kugarq

On Relating Time and Space to Size and Depth

Allan Borodin
1977 SIAM journal on computing (Print)  
Motivated by the simulations of Pratt and Stockmeyer [22] and Hartmanis and Simon [9] , it is not hard to see that the crux of our space simulation should rely on the transitive closure problem.  ...  In doing so, we relate the power of nondeterminism for space bounded computations to the depth required for the transitive closure problem.  ...  Cook for a number of important suggestions, and to A. Meyer, L. Stockmeyer and the referees for their helpful comments.  ... 
doi:10.1137/0206054 fatcat:f45h6aubu5br3cgwhdz2t6nnp4

Page 1424 of Mathematical Reviews Vol. , Issue 86d [page]

1986 Mathematical Reviews  
Terming a linear transformation ¢ of a finite- dimensional vector space irreducible if the only y-invariant sub- spaces are {0} and the whole space, the author shows that is irreducible if and only if  ...  The author’s thesis contains an example of a polynomial with Galois group G for every transitive group of degree at most 7.  ... 

The Complexity of Model Checking Mobile Ambients [chapter]

Witold Charatonik, Silvano Dal Zilio, Andrew D. Gordon, Supratik Mukhopadhyay, Jean-Marc Talbot
2001 Lecture Notes in Computer Science  
For the complexity upper-bound, we devise a new representation of processes that remains of polynomial size during process execution; this allows us to keep the model checking procedure in polynomial space  ...  Moreover, we prove PSPACEhardness of the problem for several quite simple fragments of the calculus and the logic; this suggests that there are no interesting fragments with polynomial-time model checking  ...  We write → * and ↓ * for the reflexive and transitive closure of → and ↓, respectively.  ... 
doi:10.1007/3-540-45315-6_10 fatcat:c7ntdwvsorel3cd2ythclgnxli

Noetherian Spaces in Verification [chapter]

Jean Goubault-Larrecq
2010 Lecture Notes in Computer Science  
Noetherian spaces are a topological concept that generalizes well quasiorderings.  ...  We explore applications to infinite-state verification problems, and show how this stimulated the search for infinite procedures à la Karp-Miller.  ...  A topological space is sober if and only if every irreducible closed subset is the closure ↓ of a unique point ∈ .  ... 
doi:10.1007/978-3-642-14162-1_2 fatcat:noux7wn3gfcwlkssyf2hnmavti

Page 2537 of Mathematical Reviews Vol. , Issue 83f [page]

1983 Mathematical Reviews  
Tompa, Martin 83f:68048 Two familiar transitive closure algorithms which admit no polynomial time, sublinear space i SIAM J. Comput. 11 (1982), no. 1, 130-137.  ...  It is also shown that any implementation of Warshall’s transitive closure algorithm requires 2(n) space, and that many familiar sorting algorithms exhibit similar behavior.”  ... 

On characterizations of the class PSPACE/poly

J.L. Balcázar, J. Díaz, J. Gabarró
1987 Theoretical Computer Science  
PSPACE/PO~Y is exactly the class of sets accepted by an oracle machine which uses polynomially bounded work space and logarithmically bounded oracle space. roof.  ...  Let L be in PSPACE/~~~~; then there exists a polynomially space-bounded machine M with advice h(n) of polynomial length which recognizes L.  ...  In [2,3], it is shown that y(M) is in BNP, and therefore its transitive closure y*(M) is in Ce.  ... 
doi:10.1016/0304-3975(87)90111-3 fatcat:womffvrnafa47lv5opg2zb6ks4

Any algorithm in the complex object algebra with powerset needs exponential space to compute transitive closure

Dan Suciu, Jan Paredaens
1994 Proceedings of the thirteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '94  
The Abiteboul and Beeri algebra for complex objects can express a query whose meaning is transitive closure, but the algorithm naturally associated to this query needs exponential space.  ...  Comments Abstract The Abiteboul and Beeri algebra for complex objects can express a query whose meaning is transitive closure, but the algorithm naturally associated to this query needs exponential space  ...  Acknowledgments We would like to thank Val Breazu-Tannen and Peter Buneman for their suggestions and support.  ... 
doi:10.1145/182591.182613 dblp:conf/pods/SuciuP94 fatcat:vd5gsxcpl5dwjfgrs2wpclisji

Computational methods in number theory, Part I

1984 Discrete Applied Mathematics  
Chapter 17: Superpositions of states and closure spaces. A general characterization of state superpositions. The closure space of pure states and the associated lattice structure.  ...  Properties of transition-probability spaces. The order structure arising from transition-probability spaces. Transition probabilities and the Hilbert model. Exercises. References.  ... 
doi:10.1016/0166-218x(84)90119-7 fatcat:2nvaf7k6xbhetnqpnhqkxob4xe

Computational methods in number theory, Part II

1984 Discrete Applied Mathematics  
Chapter 17: Superpositions of states and closure spaces. A general characterization of state superpositions. The closure space of pure states and the associated lattice structure.  ...  Properties of transition-probability spaces. The order structure arising from transition-probability spaces. Transition probabilities and the Hilbert model. Exercises. References.  ... 
doi:10.1016/0166-218x(84)90120-3 fatcat:yozkfg7ba5h27aak5msdkjfzue

Resolving and Exploiting the k-CFA Paradox [article]

Matthew Might, Yannis Smaragdakis, David Van Horn
2013 arXiv   pre-print
We resolve this paradox by showing that the exact same specification of k-CFA is polynomial-time for object-oriented languages yet exponential- time for functional ones: objects and closures are subtly  ...  Van Horn and Mairson proved k-CFA for k ≥ 1 to be EXPTIME-complete; hence, no polynomial-time algorithm can exist.  ...  Acknowledgments: We are grateful to Jan Midtgaard for comments and relevant references to the literature. We thank Ondřej Lhoták for valuable discussions.  ... 
arXiv:1311.4231v1 fatcat:r3rwptrj45atphjv72oopud64i
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