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Hausdorffization and polynomial twists

2010
*
Discrete and Continuous Dynamical Systems. Series A
*

We study dynamical equivalence relations on the moduli

doi:10.3934/dcds.2011.29.1405
fatcat:hft73d3dtfal3cv4fmvokcvg7a
*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. ...##
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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*...##
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Transitive Closure of a Union of Dependence Relations for Parameterized Perfectly-Nested Loops
[chapter]

2013
*
Lecture Notes in Computer Science
*

This allows us to effectively extract both fine-

doi:10.1007/978-3-642-39958-9_4
fatcat:yhsbahxwwjg5tnat6kkaebkzlq
*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. ...##
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Model checking and transitive-closure logic
[chapter]

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

doi:10.1007/3-540-63166-6_29
fatcat:pozwqznvtbc5ff7ozncmctv37i
*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. ...##
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Mantaining Dynamic Matrices for Fully Dynamic Transitive Closure
[article]

2001
*
arXiv
*
pre-print

In this paper we introduce a general framework for casting fully dynamic

arXiv:cs/0104001v1
fatcat:brp2hexcxfanvjhqzbh5kugarq
*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. ...##
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On Relating Time and Space to Size and Depth

1977
*
SIAM journal on computing (Print)
*

Motivated by the simulations of Pratt

doi:10.1137/0206054
fatcat:f45h6aubu5br3cgwhdz2t6nnp4
*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. ...##
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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. ...##
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The Complexity of Model Checking Mobile Ambients
[chapter]

2001
*
Lecture Notes in Computer Science
*

For the complexity upper-bound, we devise a new representation of processes that remains of

doi:10.1007/3-540-45315-6_10
fatcat:c7ntdwvsorel3cd2ythclgnxli
*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. ...##
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Noetherian Spaces in Verification
[chapter]

2010
*
Lecture Notes in Computer Science
*

Noetherian

doi:10.1007/978-3-642-14162-1_2
fatcat:noux7wn3gfcwlkssyf2hnmavti
*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 ∈ . ...##
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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.” ...##
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On characterizations of the class PSPACE/poly

1987
*
Theoretical Computer Science
*

PSPACE/PO~Y is exactly the class of sets accepted by an oracle machine which uses

doi:10.1016/0304-3975(87)90111-3
fatcat:womffvrnafa47lv5opg2zb6ks4
*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. ...##
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Any algorithm in the complex object algebra with powerset needs exponential space to compute transitive closure

1994
*
Proceedings of the thirteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '94
*

The Abiteboul

doi:10.1145/182591.182613
dblp:conf/pods/SuciuP94
fatcat:vd5gsxcpl5dwjfgrs2wpclisji
*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. ...##
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Computational methods in number theory, Part I

1984
*
Discrete Applied Mathematics
*

Chapter 17: Superpositions
of states

doi:10.1016/0166-218x(84)90119-7
fatcat:2nvaf7k6xbhetnqpnhqkxob4xe
*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. ...##
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Computational methods in number theory, Part II

1984
*
Discrete Applied Mathematics
*

Chapter 17: Superpositions
of states

doi:10.1016/0166-218x(84)90120-3
fatcat:yozkfg7ba5h27aak5msdkjfzue
*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. ...##
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Resolving and Exploiting the k-CFA Paradox
[article]

2013
*
arXiv
*
pre-print

We resolve this paradox by showing that the exact same specification of k-CFA is

arXiv:1311.4231v1
fatcat:r3rwptrj45atphjv72oopud64i
*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. ...
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