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Your search keyword '"Omodeo, Eugenio G."' showing total 168 results
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168 results on '"Omodeo, Eugenio G."'

1. Six equations in search of a finite-fold-ness proof

Author

Cantone, Domenico, Cuzziol, Luca, and Omodeo, Eugenio G.

Subjects
Mathematics - Number Theory, Mathematics - Logic, 03D25, 11D25
Abstract

By following the same construction pattern which Martin Davis proposed in a 1968 paper of his, we have obtained six quaternary quartic Diophantine equations that candidate as `rule-them-all' equations: proving that one of them has only a finite number of integer solutions would suffice to ensure that each recursively enumerable set admits a finite-fold polynomial Diophantine representation.

Published
2023

3. Onset and Today’s Perspectives of Multilevel Syllogistic

Author

Cantone, Domenico, Omodeo, Eugenio G., Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Cantone, Domenico, editor, and Pulvirenti, Alfredo, editor

Published
2024
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4. Complexity assessments for decidable fragments of Set Theory. IV: A quadratic reduction of constraints over nested sets to Boolean formulae

Author

Cantone, Domenico, De Domenico, Andrea, Maugeri, Pietro, and Omodeo, Eugenio G.

Subjects
Computer Science - Logic in Computer Science, Computer Science - Artificial Intelligence
Abstract

As a contribution to quantitative set-theoretic inferencing, a translation is proposed of conjunctions of literals of the forms $x=y\setminus z$, $x \neq y\setminus z$, and $z =\{x\}$, where $x,y,z$ stand for variables ranging over the von Neumann universe of sets, into unquantified Boolean formulae of a rather simple conjunctive normal form. The formulae in the target language involve variables ranging over a Boolean ring of sets, along with a difference operator and relators designating equality, non-disjointness and inclusion. Moreover, the result of each translation is a conjunction of literals of the forms $x=y\setminus z$, $x\neq y\setminus z$ and of implications whose antecedents are isolated literals and whose consequents are either inclusions (strict or non-strict) between variables, or equalities between variables. Besides reflecting a simple and natural semantics, which ensures satisfiability-preservation, the proposed translation has quadratic algorithmic time-complexity, and bridges two languages both of which are known to have an NP-complete satisfiability problem.

Published
2021

8. In Memory of Martin Davis

Author

Calvert, Wesley, Harizanov, Valentina, Omodeo, Eugenio G., Policriti, Alberto, Shlapentokh, Alexandra, Calvert, Wesley, Harizanov, Valentina, Omodeo, Eugenio G., Policriti, Alberto, and Shlapentokh, Alexandra

Abstract

The present paper gives an account for the general mathematical reader of the life and work of Martin Davis. Since two rather comprehensive autobiographical accounts and two long biographical interviews already exist, the present work focusses on Davis's scientific achievements, including work on computably enumerable sets, universal Turing machines, the hyperarithmetical hierarchy, neural networks, Hilbert's Tenth Problem, and automated reasoning.

Published
2024

10. Random Generation of Sets

Author

Omodeo, Eugenio G., Policriti, Alberto, Tomescu, Alexandru I., Omodeo, Eugenio G., Policriti, Alberto, and Tomescu, Alexandru I.

Published
2017
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12. Graphs as Transitive Sets

Author

Omodeo, Eugenio G., Policriti, Alberto, Tomescu, Alexandru I., Omodeo, Eugenio G., Policriti, Alberto, and Tomescu, Alexandru I.

Published
2017
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16. Introduction

Author

Omodeo, Eugenio G., Policriti, Alberto, Tomescu, Alexandru I., Omodeo, Eugenio G., Policriti, Alberto, and Tomescu, Alexandru I.

Published
2017
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22. Introduction

Author

Schwartz, Jacob T., Cantone, Domenico, Omodeo, Eugenio G., Schwartz, Jacob T., Cantone, Domenico, and Omodeo, Eugenio G.

Published
2011
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29. Theory-Specific Automated Reasoning

Author

Formisano, Andrea, Omodeo, Eugenio G., Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Dovier, Agostino, editor, and Pontelli, Enrico, editor

Published
2010
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30. An Environment for Specifying Properties of Dyadic Relations and Reasoning About Them II: Relational Presentation of Non-classical Logics

Author

Formisano, Andrea, Omodeo, Eugenio G., Orłowska, Ewa, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Carbonell, Jaime G., editor, Siekmann, Jörg, editor, de Swart, Harrie, editor, Orłowska, Ewa, editor, Schmidt, Gunther, editor, and Roubens, Marc, editor

Published
2006
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31. A Computerized Referee

Author

Omodeo, Eugenio G., Cantone, Domenico, Policriti, Alberto, Schwartz, Jacob T., Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Carbonell, Jaime G., editor, Siekmann, Jörg, editor, Stock, Oliviero, editor, and Schaerf, Marco, editor

Published
2006
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41. Reconciling transparency, low Δ0-complexity and axiomatic weakness in undecidability proofs.

Author

Cantone, Domenico, Omodeo, Eugenio G, and Panettiere, Mattia

Subjects
AXIOMATIC set theory, STATISTICAL decision making, SET theory
Abstract

In a first-order theory |$\varTheta $|⁠ , the decision problem for a class of formulae |$\varPhi $| is solvable if there is an algorithmic procedure that can assess whether or not the existential closure |$\varphi ^{\exists }$| of |$\varphi $| belongs to |$\varTheta $|⁠ , for any |$\varphi \in \varPhi $|⁠. In 1988, Parlamento and Policriti already showed how to tailor arguments à la Gödel to a very weak axiomatic set theory, referring them to the class of |$\varSigma _{1}$| -formulae with |$(\forall \exists \forall)_{0}$| -matrix, i.e. existential closures of formulae that contain just restricted quantifiers of the forms |$(\forall x \in y)$| and |$(\exists x \in y)$| and are writable in prenex form with at most two alternations of restricted quantifiers (the outermost quantifier being a ' |$\forall $| '). While revisiting their work, we show slightly less weak theories under which incompleteness for recursively axiomatizable extensions holds with respect to existential closures of |$(\forall \exists)_{0}$| -matrices, namely formulae with at most one alternation of restricted quantifiers. [ABSTRACT FROM AUTHOR]

Published
2023
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44. 'One equation to rule them all', revisited

Author

Cantone, Domenico and Omodeo, Eugenio G.

Subjects
03D25, single/finite-fold Diophantine representation, Pell���s equation, 11D25, Hilbert���s 10th problem, Hilbert’s 10th problem, Pell’s equation, exponential-growth relation
Abstract

If the quaternary quartic equation 9 · (u² + 7v²)² − 7 · (r² + 7s²)² = 2 (*) which M. Davis put forward in 1968 has only finitely many solutions in integers, then — it was observed by M. Davis, Yu. V. Matiyasevich, and J. Robinson in 1976 — every listable set would turn out to admit a single-fold Diophantine representation. In 1995, D. Shanks and S. S. Wagstaff conjectured that (*) has infinitely many solutions; while in doubt, it seemed wise to us to single out new candidates for the role of “rule-them-all equation”. We offer three new quaternary quartic equations, each obtained by much the same recipe which led to (*). The significance of those can be supported by arguments analogous to the ones found in Davis’s original paper; moreover, they might play a key role in settling the conjecture that every listable set has a single-fold (or, at least, a finite-fold) representation. Directly from the unproven assertion that any of the novel equations has only finitely many solutions in integers, one can construct a Diophantine relation of exponential growth, as we show in detail for one, namely 3 · (r² + 3s²)² − (u² + 3v²)² = 2, of the new candidate rule-them-all equations. An account of Julia Robinson’s earliest Diophantine reduction of exponentiation to any relation of exponential growth is also included, for the sake of self-containedness.

Published
2021

46. Preface

Author

Casagrande, Alberto, primary, Omodeo, Eugenio G., additional, and Proietti, Maurizio, additional

Published
2021
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49. A Computerized Referee

Author

Omodeo, Eugenio G., primary, Cantone, Domenico, additional, Policriti, Alberto, additional, and Schwartz, Jacob T., additional

Published
2006
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