bibHainry.bib
@inproceedings{HKMP24-lics,
title = {{Declassification Policy for Program Complexity Analysis}},
author = {Hainry, Emmanuel and Kapron, Bruce M. and Marion, Jean-Yves and P{\'e}choux, Romain},
url = {https://inria.hal.science/hal-04742085},
booktitle = {{LICS '24: 39th Annual ACM/IEEE Symposium on Logic in Computer Science}},
address = {Tallinn Estonia, France},
publisher = {{ACM}},
pages = {1-14},
year = {2024},
month = {july},
doi = {10.1145/3661814.3662100},
keywords = {Theory of computation $\rightarrow$ Complexity theory and logic ; Type theory ; Noninterference ; Declassification ; Polynomial time ; Basic Feasible Functionals ; Complexity analysis},
pdf = {https://inria.hal.science/hal-04742085v1/file/LICS24-112.pdf},
hal_id = {hal-04742085},
hal_version = {v1}
}
@inproceedings{HP23-popl,
author = {Hainry, Emmanuel and P\'{e}choux, Romain},
title = {A General Noninterference Policy for Polynomial Time},
booktitle = {Principles of Programming Languages, POPL 2023},
year = 2023,
publisher = {ACM},
volume = {7},
pages = {806--832},
doi = {10.1145/3571221},
abstract = {We introduce a new noninterference policy to capture the class of functions computable in polynomial time on an object-oriented programming language. This policy makes a clear separation between the standard noninterference techniques for the control flow and the layering properties required to ensure that each “security” level preserves polynomial time soundness, and is thus very powerful as for the class of programs it can capture. This new characterization is a proper extension of existing tractable characterizations of polynomial time based on safe recursion. Despite the fact that this noninterference policy is Π10-complete, we show that it can be instantiated to some decidable and conservative instance using shape analysis techniques.},
series = {Proc. ACM Program. Lang.},
articleno = {28},
numpages = {27},
url = {https://inria.hal.science/hal-04190355},
pdf = {https://inria.hal.science/hal-04190355/file/shapedTiering.pdf},
keywords = {Polynomial time, Noninterference, Shape Analysis, Computational Complexity}
}
@inproceedings{HPS23-fossacs,
title = {A programming language characterizing quantum polynomial time},
author = {Hainry, Emmanuel and P{\'e}choux, Romain and Silva, M{\'a}rio},
url = {https://inria.hal.science/hal-04190385},
booktitle = {Foundations of Software Science and Computation Structures (FoSSaCS 2023)},
address = {Paris, France},
year = 2023,
month = {april},
doi = {10.1007/978-3-031-30829-1_8},
pdf = {https://inria.hal.science/hal-04190385/file/paper_FBQP_revised.pdf},
hal_id = {hal-04190385},
hal_version = {v1}
}
@inproceedings{HKMP22-fossacs,
author = {Emmanuel Hainry and Bruce M. Kapron and Jean-Yves Marion and Romain P{\'{e}}choux},
title = {Complete and tractable machine-independent characterizations of second-order polytime},
booktitle = {Foundations of Software Science and Computation Structures (FoSSaCS 2022)},
series = {Lecture Notes in Computer Science},
pages = {368--388},
publisher = {Springer},
year = 2022,
doi = {10.1007/978-3-030-99253-8_19},
url = {https://hal.inria.fr/hal-03722245},
pdf = {https://hal.inria.fr/hal-03722245/file/ctcbff.pdf},
hal_id = {hal-03722245},
hal_version = {v1}
}
@article{HKMP22-lmcs,
author = {Emmanuel Hainry and Bruce M. Kapron and Jean-Yves Marion and Romain P{\'{e}}choux},
title = {A tier-based typed programming language characterizing Feasible Functionals},
year = 2022,
journal = {Logical Methods in Computer Science},
volume = 18,
number = 1,
doi = {10.46298/lmcs-18(1:33)2022},
url = {https://hal.inria.fr/hal-03722168},
pdf = {https://hal.inria.fr/hal-03722168/file/hkmplmcs.pdf},
hal_id = {hal-03722168},
hal_version = {v1}
}
@inproceedings{HJPZ21-ictac,
author = {Emmanuel Hainry and Emmanuel Jeandel and Romain P{\'{e}}choux and Olivier Zeyen},
editor = {Antonio Cerone and Peter Csaba {\"{O}}lveczky},
title = {ComplexityParser: An Automatic Tool for Certifying Poly-Time Complexity of Java Programs},
booktitle = {{ICTAC} 2021 - 18th International Colloquium on Theoretical Aspects of Computing},
address = {Nur-Sultan, Kazakhstan},
series = {Lecture Notes in Computer Science},
volume = 12819,
pages = {357--365},
publisher = {Springer},
month = {september},
year = 2021,
doi = {10.1007/978-3-030-85315-0_20},
url = {https://hal.inria.fr/hal-03337755},
pdf = {https://hal.inria.fr/hal-03337755/file/ictac-tool.pdf},
hal_id = {hal-03337755},
hal_version = {v1}
}
@inproceedings{HKMP20-lics,
title = {{A tier-based typed programming language characterizing Feasible Functionals}},
author = {Hainry, Emmanuel and Kapron, Bruce M. and Marion, Jean-Yves and P{\'e}choux, Romain},
url = {https://hal.inria.fr/hal-02881308},
booktitle = {Logic in Computer Science, LICS 2020},
address = {Saarbr{\"u}cken, Germany},
publisher = {{ACM}},
pages = {535-549},
year = {2020},
month = {july},
doi = {10.1145/3373718.3394768},
keywords = {Feasible functionals ; BFF ; implicit computational complexity ; tiering ; type-2 ; type system},
pdf = {https://hal.inria.fr/hal-02881308/file/bff-lics.pdf},
hal_id = {hal-02881308},
hal_version = {v1}
}
@inproceedings{HMP20-flops,
title = {{Polynomial time over the reals with parsimony}},
author = {Hainry, Emmanuel and Mazza, Damiano and P{\'e}choux, Romain},
url = {https://hal.inria.fr/hal-02499149},
booktitle = {Functional and Logic Programming (FLOPS 2020)},
address = {Akita, Japan},
year = {2020},
month = {april},
doi = {10.1007/978-3-030-59025-3_4},
pdf = {https://hal.inria.fr/hal-02499149/file/main.pdf},
hal_id = {hal-02499149},
hal_version = {v1}
}
@article{HP20-LMCS,
title = {{Theory of Higher Order Interpretations and Application to Basic Feasible Functions}},
author = {Hainry, Emmanuel and P{\'e}choux, Romain},
url = {https://hal.inria.fr/hal-02499206},
journal = {{Logical Methods in Computer Science}},
publisher = {{Logical Methods in Computer Science Association}},
volume = {16},
number = {4},
pages = {25},
year = {2020},
month = {december},
doi = {10.23638/LMCS-16(4:14)2020},
keywords = {Implicit computational complexity ; basic feasible functionals},
pdf = {https://hal.inria.fr/hal-02499206v2/file/1801.08350v4.pdf},
hal_id = {hal-02499206},
hal_version = {v2}
}
@article{HP18-ic,
title = {{A Type-Based Complexity Analysis of Object Oriented Programs}},
author = {Hainry, Emmanuel and P{\'e}choux, Romain},
url = {https://hal.inria.fr/hal-01712506},
journal = {{Information and Computation}},
publisher = {{Elsevier}},
series = {Information and Computation},
volume = {261},
number = {1},
pages = {78-115},
year = {2018},
month = {august},
doi = {10.1016/j.ic.2018.05.006},
keywords = {Object Oriented Program ; Type system ; complexity ; polynomial time},
pdf = {https://hal.inria.fr/hal-01712506/file/Object.pdf},
hal_id = {hal-01712506},
hal_version = {v1}
}
@inproceedings{HP17-lpar,
author = {Emmanuel Hainry and Romain P{\'e}choux},
title = {Higher order interpretation for higher order complexity},
booktitle = {LPAR-21. 21st International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
year = 2017,
editor = {Thomas Eiter and David Sands},
volume = {46},
series = {EPiC Series in Computing},
pages = {269--285},
abstract = {We design an interpretation-based theory of higher-order functions that is well-suited for the complexity analysis of a standard higher- order functional language a` la ml. We manage to express the interpretation of a given program in terms of a least fixpoint and we show that when restricted to functions bounded by higher-order polynomials, they characterize exactly classes of tractable functions known as Basic Feasible Functions at any order.},
doi = {10.29007/1tkw},
file = {:articles/HP17-lpar .pdf:PDF}
}
@article{FHHP15-tcs,
author = {F{\'{e}}r{\'{e}}e, Hugo and Hainry, Emmanuel and Hoyrup, Mathieu and P{\'{e}}choux, Romain},
title = {Characterizing polynomial time complexity of stream programs using interpretations},
journal = {Theoretical Computer Science},
year = 2015,
volume = {585},
pages = {41--54},
doi = {10.1016/j.tcs.2015.03.008},
publisher = {Elsevier}
}
@inproceedings{HP15-aplas,
title = {{Objects in Polynomial Time}},
author = {Hainry, Emmanuel and P{\'e}choux, Romain},
url = {https://hal.inria.fr/hal-01206161},
booktitle = {APLAS 2015},
address = {Pohang, South Korea},
editor = {Xinyu Feng and Sungwoo Park},
publisher = {Springer},
series = {Lecture Notes in Computer Science},
volume = {9458},
pages = {387--404},
year = 2015,
month = {november},
doi = {10.1007/978-3-319-26529-2_21},
pdf = {https://hal.inria.fr/hal-01206161/file/ICCOW.pdf},
hal_id = {hal-01206161}
}
@article{BGH13-jcss,
title = {Computation with perturbed dynamical systems},
author = {Bournez, Olivier and Gra{\c c}a, Daniel and Hainry, Emmanuel},
url = {https://hal.inria.fr/hal-00643634},
journal = {Journal of Computer and System Sciences},
publisher = {Elsevier},
volume = {79},
number = {5},
pages = {714-724},
year = 2013,
doi = {10.1016/j.jcss.2013.01.025},
keywords = {robustness ; Dynamical systems ; reachability ; computational power ; verification},
hal_id = {hal-00643634}
}
@inproceedings{HMP13-fossacs,
title = {Type-based complexity analysis for fork processes},
author = {Hainry, Emmanuel and Marion, Jean-Yves and P{\'e}choux, Romain},
url = {https://hal.inria.fr/hal-00755450},
booktitle = {Foundations of Software Science and Computation Structures (FoSSaCS 2013)},
address = {Rome, Italy},
editor = {Pfenning, Frank},
publisher = {Springer},
volume = {7794},
pages = {305-320},
year = 2013,
doi = {10.1007/978-3-642-37075-5_20},
keywords = {Implicit Computational Complexity ; Tiering ; Secure Information Flow ; Concurrent Programming ; PSpace},
hal_id = {hal-00755450}
}
@article{bgh11-ijuc,
title = {{Algebraic Characterizations of Complexity-Theoretic Classes of Real Functions}},
author = {Bournez, Olivier and Gomaa, Walid and Hainry, Emmanuel},
url = {https://hal.inria.fr/hal-00644361},
journal = {{International Journal of Unconventional Computing}},
publisher = {{Old City Publishing}},
volume = {7},
number = {5},
pages = {331-351},
year = 2011,
keywords = {Recursive Analysis ; Polynomial Time ; Algebraic Characterization ; Real Computation ; Oracle Turing Machines}
}
@inproceedings{BGH10-mfcs,
author = {Bournez, Olivier and Gra\c{c}a, Daniel S. and Hainry, Emmanuel},
title = {Robust Computations with Dynamical Systems},
booktitle = {Mathematical Foundations of Computer Science, MFCS 2010},
year = 2010,
editor = {Hlin{\v{e}}n{\'y}, Petr and Ku{\v{c}}era, Anton\'{\i}n},
volume = {6281},
series = {Lecture Notes in Computer Science},
pages = {198-208},
publisher = {Springer},
abstract = {In this paper we discuss the computational
power of Lipschitz dynamical systems which are robust to
infinitesimal perturbations. Whereas the study in [1] was done
only for not-so-natural systems from a classical mathematical
point of view (discontinuous differential equation systems,
discontinuous piecewise affine maps, or perturbed Turing
machines), we prove that the results presented there can be
generalized to Lipschitz and computable dynamical systems. In
other words, we prove that the perturbed reachability problem
(i.e. the reachability problem for systems which are subjected
to infinitesimal perturbations) is co-recursively enumerable
for this kind of systems. Using this result we show that if
robustness to infinitesimal perturbations is also required, the
reachability problem becomes decidable. This result can be
interpreted in the following manner: undecidability of
verification doesn't hold for Lipschitz, computable and robust
systems. We also show that the perturbed reachability problem
is co-r.e. complete even for C$\infty$-systems.},
doi = {10.1007/978-3-642-15155-2_19},
isbn = {978-3-642-15154-5}
}
@inproceedings{FHHP10-isaac,
author = {{F}{\'e}r{\'e}e, {H}ugo and {H}ainry, {E}mmanuel and {H}oyrup, {M}athieu and {P}{\'e}choux, {R}omain},
title = {{I}nterpretation of stream programs: characterizing type 2 polynomial time complexity},
booktitle = {{I}nternational {S}ymposium on {A}lgorithms and {C}omputation ({ISAAC})},
year = 2010,
editor = {Cheong, Ottfried and Chwa, Kyung-Wong and Park, Kunsoo},
volume = {6506},
series = {Lecture Notes in Computer Science},
pages = {291-303},
address = {{J}eju {I}sland, South Korea},
publisher = {{S}pringer},
abstract = {{W}e study polynomial time complexity of type
2 functionals. {F}or that purpose, we introduce a first order
functional stream language. {W}e give criteria, named
well-founded, on such programs relying on second order
interpretation that characterize two variants of type 2
polynomial complexity including the {B}asic {F}easible
{F}unctions ({BFF}). {T}hese characterizations provide a new
insight on the complexity of stream programs. {F}inally, we
adapt these results to functions over the reals, a particular
case of type 2 functions, and we provide a characterization of
polynomial time complexity in {R}ecursive {A}nalysis.},
audience = {internationale },
doi = {10.1007/978-3-642-17517-6_27},
hal_id = {inria-00518381}
}
@inproceedings{BGH09-lcc,
title = {{I}mplicit complexity in recursive analysis},
author = {Bournez, Olivier and Gomaa, Walid and Hainry, Emmanuel},
abstract = {{R}ecursive analysis is a model of analog
computation which is based on type 2 {T}uring machines.
{V}arious classes of functions computable in recursive analysis
have recently been characterized in a machine independent and
algebraical context. {I}n particular nice connections between
the class of computable functions (and some of its sub and
sup-classes) over the reals and algebraically defined (sub- and
sup-) classes of {R}-recursive functions {\`{a}} la {M}oore have
been obtained. {W}e provide in this paper a framework that
allows to dive into complexity for functions over the reals.
{I}t indeed relates classical computability and complexity
classes with the corresponding classes in recursive analysis.
{T}his framework opens the field of implicit complexity of
functions over the reals. {W}hile our setting provides a new
reading of some of the existing characterizations, it also
provides new results: inspired by {B}ellantoni and {C}ook's
characterization of polynomial time computable functions, we
provide the first algebraic characterization of polynomial time
computable functions over the reals.},
language = {{A}nglais},
affiliation = {{L}aboratoire d'informatique de l'{\'e}cole polytechnique - {LIX} - {CNRS} : {UMR}7161 - {P}olytechnique - {X} - {CARTE} - {INRIA} {L}orraine - {LORIA} - {CNRS} : {UMR}7503 - {INRIA} - {U}niversit{\'e} {H}enri {P}oincar{\'e} - {N}ancy {I} - {U}niversit{\'e} {N}ancy {II} - {I}nstitut {N}ational {P}olytechnique de {L}orraine },
booktitle = {{LCC}'09 - {L}ogic and {C}omputational {C}omplexity },
address = {{L}os {A}ngeles {\'E}tats-{U}nis d'{A}m{\'e}rique },
audience = {internationale },
day = 10,
month = {august},
year = 2009,
url = {http://hal.inria.fr/inria-00429964/en/}
}
@techreport{Hai09-unpublished,
title = {{D}ecidability and {U}ndecidability in {D}ynamical {S}ystems},
author = {Hainry, Emmanuel},
abstract = {{A} computing system can be modelized in
various ways: one being in analogy with transfer functions,
this is a function that associates to an input and optionally
some internal states, an output ; another being focused on the
behaviour of the system, that is describing the sequence of
states the system will follow to get from this input to produce
the output. {T}his second kind of system can be defined by
dynamical systems. {T}hey indeed describe the ``local''
behaviour of a system by associating a configuration of the
system to the next configuration. {I}t is obviously interesting
to get an idea of the ``global'' behaviour of such a dynamical
system. {T}he questions that it raises can be for example
related to the reachability of a certain configuration or set
of configurations or to the computation of the points that will
be visited infinitely often. {T}hose questions are
unfortunately very complex: they are in most cases undecidable.
{T}his article will describe the fundamental problems on
dynamical systems and exhibit some results on decidability and
undecidability in various kinds of dynamical systems.},
language = {{A}nglais},
affiliation = {{CARTE} - {INRIA} {L}orraine - {LORIA} - {CNRS} : {UMR}7503 - {INRIA} - {U}niversit{\'e} {H}enri {P}oincar{\'e} - {N}ancy {I} - {U}niversit{\'e} {N}ancy {II} - {I}nstitut {N}ational {P}olytechnique de {L}orraine },
institution = {{CARTE} - {INRIA} {L}orraine - {LORIA} - {CNRS} : {UMR}7503 - {INRIA} - {U}niversit{\'e} {H}enri {P}oincar{\'e} - {N}ancy {I} - {U}niversit{\'e} {N}ancy {II} - {I}nstitut {N}ational {P}olytechnique de {L}orraine },
pages = 27,
type = {Research Report},
year = 2009,
url = {http://hal.inria.fr/inria-00429965/en/}
}
@inproceedings{Hai08-cie,
author = {Hainry, Emmanuel},
title = {Reachability in Linear Dynamical Systems},
booktitle = {CiE 2008: Logic and Theory of Algorithms},
year = 2008,
editor = {Beckmann, Arnold and Dimitracopoulos, Costas and L{\"o}we, Benedikt},
volume = {5028},
series = {Lecture Notes in Computer Science},
pages = {241--250},
abstract = {Dynamical systems allow to modelize various phenomena or
processes by only describing their local behaviour. The study of
dynamical systems aims at knowing more on the global behaviour.
Checking the reachability of a point is a fundamental problem. In
this document, using results from the algebraic numbers theory such
as Gelfond-Schneider's theorem, we will show that this problem that
is undecidable in the general case is in fact decidable for a
natural class of continuous-time dynamical systems: linear
systems.},
doi = {10.1007/978-3-540-69407-6_28}
}
@inproceedings{Hai08-uc,
author = {Hainry, Emmanuel},
title = {Computing omega-limit Sets in Linear Dynamical Systems},
booktitle = {Unconventional Computing, UC 2008},
year = 2008,
editor = {Calude, Cristian S. and Costa, Jos\'{e} F\'{e}lix and Freund, Rudolf and Oswald, Marion and Rozenberg, Grzegorz},
volume = {5204},
series = {Lecture Notes in Computer Science},
pages = {83--95},
abstract = {Dynamical systems allow to modelize various phenomena or
processes by only describing their local behaviour. It is an important
matter to study the global and the limit behaviour of such systems.
A possible description of this limit behaviour is via the
omega-limit set: the set of points that can be limit of
subtrajectories. The omega-limit set is in general uncomputable. It
can be a set highly difficult to apprehend. Some systems have for
example a fractal omega-limit set. However, in some specific cases,
this set can be computed. This problem is important to verify
properties of dynamical systems, in particular to predict its
collapse or its infinite expansion. We prove in this paper that
for linear continuous time dynamical systems, it is in fact
computable. More, we also prove that the $\omega$-limit set is
a semi-algebraic set. The algorithm to compute this set can
easily be derived from this proof.},
doi = {10.1007/978-3-540-85194-3_9}
}
@article{bcgh07-jcomp,
author = {Bournez, Olivier and Campagnolo, Manuel L. and Gra\c{c}a, Daniel S. and Hainry, Emmanuel},
title = {Polynomial differential equations compute all real computable functions on computable compact intervals},
journal = {Journal of Complexity},
year = 2007,
volume = {23},
number = {3},
pages = {317--335},
abstract = {In the last decade, there have been several attempts to
understand the relations between the many models of analog computation.
Unfortunately, most models are not equivalent. Euler's Gamma
function, which is computable according to computable analysis, but
that cannot be generated by Shannon's General Purpose Analog
Computer (GPAC), has often been used to argue that the GPAC is less
powerful than digital computation. However, when computability with
GPACs is not restricted to real-time generation of functions, it
has been shown recently that Gamma becomes computable by a GPAC.
Here we extend this result by showing that, in an appropriate
framework, the GPAC and computable analysis are actually equivalent
from the computability point of view, at least in compact
intervals. Since GPACs are equivalent to systems of polynomial
differential equations then we show that all real computable
functions over compact intervals can be defined by such models.},
doi = {10.1016/j.jco.2006.12.005},
file = {:articles/BouCamGra06a.pdf:PDF},
keywords = {Analog computation; Computable analysis; General Purpose Analog Computer; Church--Turing thesis; Differential equations},
local-url = {file://localhost/Users/manu/Documents/articles/BouCamGra06a.pdf}
}
@inproceedings{bh07-mcu,
author = {Bournez, Olivier and Hainry, Emmanuel},
title = {On the computational capabilities of several models},
booktitle = {Machines, Computations, and Universality - MCU 2007, Orl\'{e}ans, France},
year = 2007,
editor = {Durand-Lose, J\'{e}r\^{o}me and Margenstern, Maurice},
volume = {4664},
series = {Lecture Notes in Computer Science},
pages = {12-23},
publisher = {Springer},
abstract = {We review some results about the computational
power of several computational models. Considered models have in common
to be related to continuous dynamical systems.},
doi = {10.1007/978-3-540-74593-8_2}
}
@inproceedings{bcgh06-tamc,
author = {Bournez, Olivier and Campagnolo, Manuel L. and Gra{\c{c}}a, Daniel S. and Hainry, Emmanuel},
title = {The General Purpose Analog Computer and Computable Analysis are Two Equivalent Paradigms of Analog Computation},
booktitle = {Theory and Applications of Models of Computation, TAMC 2006},
year = 2006,
editor = {Cai, Jin-Yi and Cooper, S. Barry and Li, Angsheng},
volume = {3959},
series = {Lecture Notes in Computer Science},
pages = {631 -- 643},
publisher = {Springer},
abstract = {In this paper we revisit one of the first models of analog
computation, Shannon's General Purpose Analog Computer (GPAC). The GPAC
has often been argued to be weaker than computable analysis. As
main contribution, we show that if we change the notion of
GPAC-computability in a natural way, we compute exactly all real
computable functions (in the sense of computable analysis).
Moreover, since GPACs are equivalent to systems of polynomial
differential equations then we show that all real computable
functions can be defined by such models.},
doi = {10.1007/11750321_60},
file = {:articles/BouCamGra06.pdf:PDF},
local-url = {file://localhost/Users/manu/Documents/articles/BouCamGra06.pdf}
}
@article{bh06-fi,
affiliation = {PROTHEO [INRIA Lorraine - LORIA]},
author = {Bournez, Olivier and Hainry, Emmanuel},
journal = {Fundamenta Informaticae},
local-url = {file://localhost/Users/manu/Documents/articles/BouHai06.pdf},
number = 4,
pages = {409--433},
publisher = {Annales Societatis Mathematicae Polonae},
title = {Recursive Analysis Characterized as a Class of Real Recursive Functions},
url = {http://hal.inria.fr/inria-00000515/en/},
volume = 74,
year = 2006,
abstract = {Recently, using a limit schema, we presented an analog and
machine independent algebraic characterization of elementarily
computable functions over the real numbers in the sense of
recursive analysis. In a dierent and orthogonal work, we proposed a
minimization schema that allows to provide a class of real
recursive functions that corresponds to extensions of computable
functions over the integers. Mixing the two approaches we prove
that computable functions over the real numbers in the sense of
recursive analysis can be characterized as the smallest class of
functions that contains some basic functions, and closed by
composition, linear integration, minimization and limit schema. }
}
@phdthesis{hainry06,
author = {Hainry, Emmanuel},
month = {december},
year = 2006,
school = {Institut National Polytechnique de Lorraine},
title = {Mod\`{e}les de calcul sur les r\'{e}els, r\'{e}sultats de comparaison},
type = {{PhD} Thesis},
local-url = {file://localhost/Users/manu/Documents/articles/Hai06.pdf},
url = {https://members.loria.fr/ehainry/papers/manuscrit.pdf},
abstract = {Il existe de nombreux mod\`{e}les de calcul sur les r\'{e}els. Ces
diff\'{e}rents mod\`{e}les calculent diverses fonctions, certains sont plus
puissants que d'autres, certains sont deux \`{a} deux incomparables. Le
calcul sur les r\'{e}els est donc de ce point de vue bien diff\'{e}rent du
calcul sur les entiers qui est unifi\'{e} par la th\`{e}se de Church-Turing
qui affirme que tous les mod\`{e}les raisonnables calculent les m^{e}mes
fonctions.
Les r\'{e}sultats de cette th\`{e}se sont de deux sortes. Premi\`{e}rement,
nous montrons des \'{e}quivalences entre les fonctions r\'{e}cursivement
calculables et une certaine classe de fonctions
$\mathbb{R}$-r\'{e}cursives et entre les fonctions {GPAC}-calculables et
les fonctions r\'{e}cursivement calculables. Ces deux r\'{e}sultats ne sont
cependant valables que si les fonctions pr\'{e}sentent quelques
caract\'{e}ristiques : elles doivent ^{e}tre d\'{e}finies sur un compact et dans
le premier cas ^{e}tre de classe $\mathscr{C}^2$. Deuxi\`{e}mement, nous
montrons \'{e}galement une hi\'{e}rarchie de classes de fonctions
$\mathbb{R}$-r\'{e}cursives qui caract\'{e}risent les fonctions
\'{e}l\'{e}mentairement calculables, les fonctions $\mathscr{E}_n$-calculables
pour $n\geq3$ (o\`{u} les $\mathcal{E}_n$ sont les fonctions de la
hi\'{e}rarchie de Grzegorczyk), et des fonctions r\'{e}cursivement
calculables. Ce r\'{e}sultat utilise un op\'{e}rateur de limite dont nous
avons prouv\'{e} la g\'{e}n\'{e}ralit\'{e} en montrant qu'il transf\`{e}re une inclusion
sur la partie discr\`{e}te des fonctions en une inclusion sur les
fonctions sur les r\'{e}els elles-m^{e}mes.
Ces r\'{e}sultats constituent donc une avanc\'{e}e vers une \'{e}ventuelle
unification des mod\`{e}les de calcul sur les r\'{e}els.},
keywords = {Analyse r\'{e}cursive, calculabilit\'{e} r\'{e}elle, fonctions \'{e}l\'{e}mentaires, hi\'{e}rarchie de Grzegorczyk, General Purpose Analog Computer}
}
@inproceedings{bh04-mcu,
author = {Bournez, Olivier and Hainry, Emmanuel},
booktitle = {Machines, Computations, and Universality, MCU 2004},
editor = {Margenstern, Maurice},
doi = {10.1007/978-3-540-31834-7_9},
local-url = {file://localhost/Users/manu/Documents/articles/BouHai04.pdf},
loria = {bournez04c,A04-R-290},
pages = {116-127},
publisher = {Springer},
series = {Lecture Notes in Computer Science},
title = {Real Recursive Functions and Real Extentions of Recursive Functions},
volume = {3354},
year = 2005,
abstract = {Recently, functions over the reals that extend elementarily
computable functions over the integers have been proved to correspond
to the smallest class of real functions containing some basic
functions and closed by composition and linear integration. We
extend this result to all computable functions: functions over the
reals that extend total recursive functions over the integers are
proved to correspond to the smallest class of real functions
containing some basic functions and closed by composition, linear
integration and a very natural unique minimization schema.}
}
@article{bh05-tcs,
author = {Bournez, Olivier and Hainry, Emmanuel},
title = {Elementary computable functions over the real numbers and {R}-sub-recursive functions},
journal = {Theoretical Computer Science},
year = 2005,
volume = {348},
number = {2-3},
pages = {130--147},
month = {december},
abstract = {We present an analog and machine-independent algebraic
characterization of elementarily computable functions over the real
numbers in the sense of recursive analysis: we prove that they
correspond to the smallest class of functions that contains some
basic functions, and closed by composition, linear integration, and
a simple limit schema. We generalize this result to all higher levels
of the Grzegorczyk Hierarchy. This paper improves several previous
partial characterizations and has a dual interest:
* Concerning recursive analysis, our results provide
machine-independent characterizations of natural classes of
computable functions over the real numbers, allowing to define
these classes without usual considerations on higher-order (type 2)
Turing machines.
* Concerning analog models, our results provide a characterization
of the power of a natural class of analog models over the real
numbers and provide new insights for understanding the relations
between several analog computational models.},
doi = {10.1016/j.tcs.2005.09.010},
keywords = {Analog computation; Recursive analysis; Real recursive functions; Computability; Analysis},
local-url = {file://localhost/Users/manu/Documents/articles/BouHai05.pdf}
}
@inproceedings{bh04-appsem,
author = {Bournez, Olivier and Hainry, Emmanuel},
title = {An analog Characterization of Elementarily Computable Functions Over the Real Numbers},
booktitle = {{2nd APPSEM II Workshop - APPSEM'2004, Tallinn, Estonia}},
crinnumber = {A04-R-289},
category = {3},
equipe = {PROTHEO},
year = 2004,
month = {april},
url = {http://www.loria.fr/publications/2004/A04-R-289/A04-R-289.ps},
keywords = {analog models, complexity, computability},
abstract = {We present an analog and machine-independent algebraic
characterizations of elementarily computable functions over the real
numbers in the sense of recursive analysis\,: we prove that they
correspond to the smallest class of functions that contains some
basic functions, and closed by composition, linear integration, and
a simple limit schema. We generalize this result to all higher
levels of the Grzegorczyk Hierarchy. Concerning recursive analysis,
our results provide machine-independent characterizations of natural
classes of computable functions over the real numbers, allowing to
define these classes without usual considerations on higher-order
(type 2) Turing machines. Concerning analog models, our results
provide a characterization of the power of a natural class of
analog models over the real numbers.}
}
@inproceedings{bh04-icalp,
author = {Bournez, Olivier and Hainry, Emmanuel},
booktitle = {International Colloquium on Automata, Languages and Programming (ICALP 2004)},
editor = {D\'{i}az, Josep and Karhum{\"a}ki, Juhani and Lepist{\"o}, Arto and Sannella, Donald},
local-url = {file://localhost/Users/manu/Documents/articles/BouHai04a.pdf},
doi = {10.1007/978-3-540-27836-8_25},
pages = {269-280},
series = {Lecture Notes in Computer Science},
title = {An analog characterization of elementary computable functions over the real numbers},
volume = {3142},
year = 2004,
abstract = {We present an analog and machine-independent algebraic
characterization of elementarily computable functions over the real
numbers in the sense of recursive analysis: we prove that they
correspond to the smallest class of functions that contains some
basic functions, and closed by composition, linear integration, and
a simple limit schema. We generalize this result to all higher
levels of the Grzegorczyk Hierarchy. Concerning recursive
analysis, our results provide machine-independent characterizations
of natural classes of computable functions over the real numbers,
making it possible to define these classes without usual considerations
on higher-order (type 2) Turing machines. Concerning analog models,
our results provide a characterization of the power of a natural class
of analog models over the real numbers.}
}
@techreport{hainry03,
author = {Hainry, Emmanuel},
title = {Fonctions r{\'e}elles calculables et fonctions {R}-r{\'e}cursives},
institution = {ENS Lyon},
year = 2003,
type = {Stage de DEA},
month = {july},
url = {http://www.loria.fr/publications/2003/A03-R-347/A03-R-347.ps},
crinnumber = {A03-R-347},
equipe = {PROTHEO},
keywords = {computability, computation over reals, elementary functions, real rcomputable functions},
abstract = {On d{\'e}finit des op{\'e}rateurs de limites sur les
fonctions. A l'aide de ces op{\'e}rateurs, on d{\'e}finit de nouvelles
classes de fonctions par cl{\^o}ture. On compare ces classes avec
les fonctions {\'e}l{\'e}mentairement calculables (d{\'e}finies
{\`a} partir de machines de Turing). On obtient ainsi une
caract{\'e}risation des fonctions {\'e}l{\'e}mentairement calculables
sous forme de cl{\^o}ture.}
}