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Page 3059 of Mathematical Reviews Vol. , Issue 96e [page]

1996 Mathematical Reviews  
Andrews, NB, 1977), 237-277, North- Holland, Amsterdam, 1978; MR 80f:68015], and uses neededness (or dependency) information to guide the fixpoint iteration, as for instance in Kildall’s early algorithm  ...  Cousot’s chaotic iteration [Formal description of programming concepts (St.  ... 

A versatile class of prototype dynamical systems for complex bifurcation cascades of limit cycles

Bulcsú Sándor, Claudius Gros
2015 Scientific Reports  
The prototype system consist of a 2d-dimensional dynamical system with friction forces f(V(x)) functionally dependent exclusively on the mechanical potential V(x), which is typically characterized, here  ...  , by a finite number of local minima.  ...  Acknowledgements The work of B.S. was supported by the European Union and the State of Hungary, co-financed by the European Social Fund in the framework of TÁMOP 4.2.4.A/2-11-1-2012-0001 National Excellence  ... 
doi:10.1038/srep12316 pmid:26198731 pmcid:PMC4510578 fatcat:s7fxltk2qbaormknth3q35wrga

Page 2955 of Mathematical Reviews Vol. , Issue 95e [page]

1995 Mathematical Reviews  
Bloom (1-STIT; Hoboken, NJ) 95e:68139 68Q60 68N17 Jorgensen, Niels (DK-ROSK; Roskilde) Chaotic fixpoint iteration guided by dynamic dependency.  ...  The proposed algorithm employs a variant of chaotic iteration, and is based on what may be termed a dynamic dependency relation.  ... 

Abstract interpretation and application to logic programs

Patrick Cousot, Radhia Cousot
1992 The Journal of Logic Programming  
When a fixpoint is reached, the chaotic iterations are stabilized so that Ifp F# =XPm.  ...  Finally, since the widening is not necessarily monotone, proposition 28 on chaotic iterations no longer applies so that the precision on the result may depend upon the chaotic iteration strategy which  ... 
doi:10.1016/0743-1066(92)90030-7 fatcat:xrgsohne6nebhchwcsk7khucma

Efficiently intertwining widening and narrowing [article]

Gianluca Amato, Francesca Scozzari, Helmut Seidl, Kalmer Apinis, Vesal Vojdani
2015 arXiv   pre-print
In order to compute reasonably precise post-fixpoints of the resulting systems of equations, Cousot and Cousot have suggested accelerated fixpoint iteration by means of widening and narrowing.  ...  In case the right-hand sides of equations are monotonic, however, we can always apply narrowing whenever we have reached a post-fixpoint for an equation.  ...  These loop heads are dynamically detected and recomputed depending on the status of the fixpoint computation.  ... 
arXiv:1503.00883v1 fatcat:6u2slvmru5c6bjankcsva2meau

Page 2356 of Mathematical Reviews Vol. , Issue 95d [page]

1995 Mathematical Reviews  
algorithms: practical efficiency for the abstract interpreta- tion of Prolog (15-26); Niels Jorgensen, Chaotic fixpoint iteration guided by dynamic dependency (27-44); Alex Ferguson and John Hughes [R  ...  57264-3 The twenty-four papers in this collection include the following: Baudouin Le Charlier, Olivier Degimbe, Laurent Michel and Pas- cal Van Hentenryck, Optimization techniques for general purpose fixpoint  ... 

Incremental and Modular Context-sensitive Analysis [article]

Isabel Garcia-Contreras, Jose F. Morales, Manuel V. Hermenegildo
2020 arXiv   pre-print
This has been achieved to date through incremental global analysis fixpoint algorithms that achieve cost reductions at fine levels of granularity, such as changes in program lines.  ...  This is equivalent to obtaining the least fixed point by chaotic iteration [16] . Adding clauses to a module.  ...  That is, the fixpoint of the new program's data flow equations is found by starting iteration from the fixpoint of the old program's data flow equations.  ... 
arXiv:1804.01839v5 fatcat:dedzgwfxdzgznczgtfuq72r4s4

How to combine widening and narrowing for non-monotonic systems of equations

Kalmer Apinis, Helmut Seidl, Vesal Vojdani
2013 SIGPLAN notices  
In order to compute reasonably precise post-fixpoints of the resulting systems of equations, Cousot and Cousot have suggested accelerated fixpoint iteration by means of widening and narrowing [6, 7] .  ...  A narrowing iteration to improve a given post-fixpoint, additionally, must assume that all right-hand sides are monotonic. The latter assumption, though, is not met in presence of widening.  ...  The last author is partially supported by the Estonian Science Foundation (EstSF) under grant n°8421.  ... 
doi:10.1145/2499370.2462190 fatcat:ks7cfesfwfgodkxanmjm4zqtuy

How to combine widening and narrowing for non-monotonic systems of equations

Kalmer Apinis, Helmut Seidl, Vesal Vojdani
2013 Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation - PLDI '13  
In order to compute reasonably precise post-fixpoints of the resulting systems of equations, Cousot and Cousot have suggested accelerated fixpoint iteration by means of widening and narrowing [6, 7] .  ...  A narrowing iteration to improve a given post-fixpoint, additionally, must assume that all right-hand sides are monotonic. The latter assumption, though, is not met in presence of widening.  ...  The last author is partially supported by the Estonian Science Foundation (EstSF) under grant n°8421.  ... 
doi:10.1145/2491956.2462190 dblp:conf/pldi/ApinisSV13 fatcat:4bmp5rcdwjfovjtzoasjuzkbkq

Improving the results of program analysis by abstract interpretation beyond the decreasing sequence

Rémy Boutonnet, Nicolas Halbwachs
2017 Formal methods in system design  
In a previous paper, we proposed a method to improve a fixpoint after its computation.  ...  It is generally admitted that, when the decreasing sequence reaches a fixpoint, it cannot be improved further.  ...  computing a decreasing sequence, by iterating the function without widening.  ... 
doi:10.1007/s10703-017-0310-y fatcat:2m62w5xycjblnixxpl3auuniam

NOISE-INDUCED CHAOS: A CONSEQUENCE OF LONG DETERMINISTIC TRANSIENTS

TAMÁS TÉL, YING-CHENG LAI, MÁRTON GRUIZ
2008 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering  
The existence of a deterministic nonattracting chaotic set, and of chaotic transients, underlying noise-induced chaos is illustrated by examples, among others by a population dynamical model.  ...  We argue that transient chaos in deterministic dynamical systems is a major source of noiseinduced chaos.  ...  This research was supported by the OTKA grants T047233 and TS044839. Y.-C. Lai was supported by AFOSR under Grant No. FA9550-06-1-0024.  ... 
doi:10.1142/s0218127408020422 fatcat:xgugcimenfd4pebzjqrfaxvrhi

Abstract Interpretation Frameworks

PATRICK COUSOT, RADHIA COUSOT
1992 Journal of Logic and Computation  
Furthermore we study various notions of widening and narrowing as a means of obtaining convergence in the iterations used in abstract interpretation.  ...  It is theoretically always possible to satisfy this hypothesis, by adding more properties to the abstract domain.  ...  This work was supported in part by Esprit BRA 3124 Sémantique and CNRS PRC C 3 .  ... 
doi:10.1093/logcom/2.4.511 fatcat:txa7gamtivf3ld6f3taywf7xnu

Why does Astrée scale up?

Patrick Cousot, Radhia Cousot, Jérôme Feret, Laurent Mauborgne, Antoine Miné, Xavier Rival
2009 Formal methods in system design  
Abstract interpreter Fixpoint iterator Static analyses reduce to computing fixpoint approximations of dynamic systems [15] , and they differ in the way the system is posed, the way it is solved and  ...  In general, a fixpoint iteration with convergence acceleration by widening is necessary to ensure termination.  ... 
doi:10.1007/s10703-009-0089-6 fatcat:lf5bl7rtznfjtlriqu62gvs35m

Resonance-Assisted Tunneling in Mixed Regular–Chaotic Systems [chapter]

Amaury Mouchet, Denis Ullmo
2011 Dynamical Tunneling  
We furthermore acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) through the Forschergruppe FOR760 "Scattering systems with complex dynamics".  ...  For mixed regular-chaotic systems, the validity of this "chaos-assisted" tunneling picture was essentially confirmed by successfully modeling the chaotic part of the quantum dynamics with a random matrix  ...  If one can explicitly construct a good integrable approximation H reg ≡ H 0 (p, q) of the time-dependent dynamics (see Sec. 8.2.1), this allows one, by quantum or semiclassical diagonalization, to determine  ... 
doi:10.1201/b10712-9 fatcat:s6357bsknbgo3mhxuzacbzc5ry

Resonance-assisted tunneling in mixed regular-chaotic systems [article]

Peter Schlagheck, Amaury Mouchet, Denis Ullmo
2011 arXiv   pre-print
We present a comprehensive theory of resonance-assisted tunneling in quantum systems that exhibit a mixed regular-chaotic classical phase space structure.  ...  derive a more precise expression for the effective coupling matrix elements that induce the resonance-assisted tunneling process, and we take into account the influence of partial barriers within the chaotic  ...  We furthermore acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) through the Forschergruppe FOR760 "Scattering systems with complex dynamics".  ... 
arXiv:1105.5362v1 fatcat:olardgx3rna5nbzest34yy7taq
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