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Documents authored by Oitavem, Isabel

Document
DOI: 10.4230/LIPIcs.CSL.2024.10
Enumerating Error Bounded Polytime Algorithms Through Arithmetical Theories

Authors: Melissa Antonelli, Ugo Dal Lago, Davide Davoli, Isabel Oitavem, and Paolo Pistone

Published in: LIPIcs, Volume 288, 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)

Abstract
We consider a minimal extension of the language of arithmetic, such that the bounded formulas provably total in a suitably-defined theory à la Buss (expressed in this new language) precisely capture polytime random functions. Then, we provide two new characterizations of the semantic class BPP obtained by internalizing the error-bound check within a logical system: the first relies on measure-sensitive quantifiers, while the second is based on standard first-order quantification. This leads us to introduce a family of effectively enumerable subclasses of BPP, called BPP_T and consisting of languages captured by those probabilistic Turing machines whose underlying error can be proved bounded in T. As a paradigmatic example of this approach, we establish that polynomial identity testing is in BPP_T, where T = IΔ₀+Exp is a well-studied theory based on bounded induction.
Cite as

Melissa Antonelli, Ugo Dal Lago, Davide Davoli, Isabel Oitavem, and Paolo Pistone. Enumerating Error Bounded Polytime Algorithms Through Arithmetical Theories. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{antonelli_et_al:LIPIcs.CSL.2024.10,
  author =	{Antonelli, Melissa and Dal Lago, Ugo and Davoli, Davide and Oitavem, Isabel and Pistone, Paolo},
  title =	{{Enumerating Error Bounded Polytime Algorithms Through Arithmetical Theories}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{10:1--10:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-310-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{288},
  editor =	{Murano, Aniello and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.10},
  URN =		{urn:nbn:de:0030-drops-196538},
  doi =		{10.4230/LIPIcs.CSL.2024.10},
  annote =	{Keywords: Bounded Arithmetic, Randomized Computation, Implicit Computational Complexity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.35
A Recursion-Theoretic Characterization of the Probabilistic Class PP

Authors: Ugo Dal Lago, Reinhard Kahle, and Isabel Oitavem

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
Probabilistic complexity classes, despite capturing the notion of feasibility, have escaped any treatment by the tools of so-called implicit-complexity. Their inherently semantic nature is of course a barrier to the characterization of classes like BPP or ZPP, but not all classes are semantic. In this paper, we introduce a recursion-theoretic characterization of the probabilistic class PP, using recursion schemata with pointers.
Cite as

Ugo Dal Lago, Reinhard Kahle, and Isabel Oitavem. A Recursion-Theoretic Characterization of the Probabilistic Class PP. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 35:1-35:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{dallago_et_al:LIPIcs.MFCS.2021.35,
  author =	{Dal Lago, Ugo and Kahle, Reinhard and Oitavem, Isabel},
  title =	{{A Recursion-Theoretic Characterization of the Probabilistic Class PP}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{35:1--35:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.35},
  URN =		{urn:nbn:de:0030-drops-144754},
  doi =		{10.4230/LIPIcs.MFCS.2021.35},
  annote =	{Keywords: Implicit complexity, tree-recursion, probabilistic classes, polynomial time, PP}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.18
A Recursion-Theoretic Characterisation of the Positive Polynomial-Time Functions

Authors: Anupam Das and Isabel Oitavem

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
We extend work of Lautemann, Schwentick and Stewart [Clemens Lautemann et al., 1996] on characterisations of the "positive" polynomial-time predicates (posP, also called mP by Grigni and Sipser [Grigni and Sipser, 1992]) to function classes. Our main result is the obtention of a function algebra for the positive polynomial-time functions (posFP) by imposing a simple uniformity constraint on the bounded recursion operator in Cobham's characterisation of FP. We show that a similar constraint on a function algebra based on safe recursion, in the style of Bellantoni and Cook [Stephen Bellantoni and Stephen A. Cook, 1992], yields an "implicit" characterisation of posFP, mentioning neither explicit bounds nor explicit monotonicity constraints.
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Anupam Das and Isabel Oitavem. A Recursion-Theoretic Characterisation of the Positive Polynomial-Time Functions. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{das_et_al:LIPIcs.CSL.2018.18,
  author =	{Das, Anupam and Oitavem, Isabel},
  title =	{{A Recursion-Theoretic Characterisation of the Positive Polynomial-Time Functions}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{18:1--18:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.18},
  URN =		{urn:nbn:de:0030-drops-96851},
  doi =		{10.4230/LIPIcs.CSL.2018.18},
  annote =	{Keywords: Monotone complexity, Positive complexity, Function classes, Function algebras, Recursion-theoretic characterisations, Implicit complexity, Logic}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.CSL.2013.24
From determinism, non-determinism and alternation to recursion schemes for P, NP and Pspace (Invited Talk)

Authors: Isabel Oitavem

Published in: LIPIcs, Volume 23, Computer Science Logic 2013 (CSL 2013)

Abstract
Our goal is to approach the classes of computational complexity P, NP, and Pspace in a recursion-theoretic manner. Here we emphasize the connection between the structure of the recursion schemes and the underlying models of computation.
Cite as

Isabel Oitavem. From determinism, non-determinism and alternation to recursion schemes for P, NP and Pspace (Invited Talk). In Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 23, pp. 24-27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{oitavem:LIPIcs.CSL.2013.24,
  author =	{Oitavem, Isabel},
  title =	{{From determinism, non-determinism and alternation to recursion schemes for P, NP and Pspace}},
  booktitle =	{Computer Science Logic 2013 (CSL 2013)},
  pages =	{24--27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-60-6},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{23},
  editor =	{Ronchi Della Rocca, Simona},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2013.24},
  URN =		{urn:nbn:de:0030-drops-41865},
  doi =		{10.4230/LIPIcs.CSL.2013.24},
  annote =	{Keywords: Computational complexity, Recursion schemes, P, NP, Pspace}
}
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