Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.53 (2021)https://www.openstarts.units.it/handle/10077/312132024-11-04T04:41:35Z2024-11-04T04:41:35Z321Prefacehttps://www.openstarts.units.it/handle/10077/335052022-03-17T22:32:11Z2021-01-01T00:00:00Zdc.title: Preface
2021-01-01T00:00:00ZForewordFonda, AlessandroMezzetti, EmiliaOmari, Pierpaolohttps://www.openstarts.units.it/handle/10077/335042022-03-17T22:32:09Z2021-01-01T00:00:00Zdc.title: Foreword
dc.contributor.author: Fonda, Alessandro; Mezzetti, Emilia; Omari, Pierpaolo
2021-01-01T00:00:00ZRendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.53 (2021)Università degli Studi di Trieste, Dipartimento di Matematica e Informaticahttps://www.openstarts.units.it/handle/10077/335022022-03-18T09:34:19Z2021-01-01T00:00:00Zdc.title: Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.53 (2021)
dc.contributor.author: Università degli Studi di Trieste, Dipartimento di Matematica e Informatica
dc.description.abstract: The journal Rendiconti dell’Istituto di Matematica dell’Università di Trieste was founded in 1969 by Arno Predonzan, with the aim of publishing original research articles in all fields of mathematics. Rendiconti dell’Istituto di Matematica dell’Universit`a di Trieste has been the first Italian mathematical journal to be published also on-line. The access to the electronic version of the journal is free. All published articles are available on-line. In 2008 the Dipartimento di Matematica e Informatica, the owner of the journal, decided to renew it. The name of the journal however remained unchanged, but the subtitle An International Journal of Mathematics was added. The journal can be obtained by subscription, or by reciprocity with other similar journals. Currently more than 100 exchange agreements with mathematics departments and institutes around the world have been entered in. The articles published by Rendiconti dell’Istituto di Matematica dell’Universit`a di Trieste are reviewed/indexed by MathSciNet, Zentralblatt Math, Scopus, OpenStarTs.
2021-01-01T00:00:00ZThe Euclidean UniverseBenci, Vierihttps://www.openstarts.units.it/handle/10077/333152024-08-17T00:07:52Z2021-01-01T00:00:00Zdc.title: The Euclidean Universe
dc.contributor.author: Benci, Vieri
dc.description.abstract: We introduce a mathematical structure called Euclidean Universe. This structure provides a basic framework for Non- Archimedean Mathematics and Nonstandard Analysis.
2021-01-01T00:00:00Z“One equation to rule them all”, revisitedCantone, DomenicoOmodeo, Eugenio G.https://www.openstarts.units.it/handle/10077/333142024-08-14T00:10:28Z2021-01-01T00:00:00Zdc.title: “One equation to rule them all”, revisited
dc.contributor.author: Cantone, Domenico; Omodeo, Eugenio G.
dc.description.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.
2021-01-01T00:00:00ZCongruences for stochastic automataDoberkat, Ernst-Erichhttps://www.openstarts.units.it/handle/10077/333132024-08-17T00:02:01Z2021-01-01T00:00:00Zdc.title: Congruences for stochastic automata
dc.contributor.author: Doberkat, Ernst-Erich
dc.description.abstract: Congruences for stochastic automata are defined, the corresponding factor automata are constructed and investigated for automata over analytic spaces. We study the behavior under finite and infinite streams. Congruences consist of multiple parts, it is shown that factoring can be undertaken in multiple steps, guided by these parts.
2021-01-01T00:00:00ZSqueezing multisets into real numbersCantone, DomenicoPolicriti, Albertohttps://www.openstarts.units.it/handle/10077/333122024-08-16T00:12:42Z2021-01-01T00:00:00Zdc.title: Squeezing multisets into real numbers
dc.contributor.author: Cantone, Domenico; Policriti, Alberto
dc.description.abstract: In this paper we study the encoding
$\mathbb{R}_A(x) = \sum_{y\in x} 2^{-\mathbb{R}_A(y)}$,
mapping hereditarily finite sets and hypersets - hereditarily finite
sets admitting circular chains of memberships - into real numbers.
The map $\mathbb{R}_A$ somewhat generalizes the well-known Ackermann's
encoding
$\mathbb{N}_A(x) = \sum_{y\in x} 2^{\mathbb{N}_A(y)}$,
whose co-domain is $\mathbb{N}$, to nonnegative real numbers.
In this work we define and study the further natural extension of the
map $\mathbb{R}_A$ to the so-called multisets. Such an extension is
simply obtained by multiplying by $k$ the code of each element having
multiplicity equal to $k$.
We prove that, under a rather natural injectivity assumption of
$\mathbb{R}_A$ on the universe of multisets, the map $\mathbb{R}_A$
sends almost all multisets into transcendental numbers.
2021-01-01T00:00:00ZEpistemic logics for modeling group dynamics of cooperative agents, and aspects of Theory of MindCostantini, Stefaniahttps://www.openstarts.units.it/handle/10077/333112024-08-16T00:12:12Z2021-01-01T00:00:00Zdc.title: Epistemic logics for modeling group dynamics of cooperative agents, and aspects of Theory of Mind
dc.contributor.author: Costantini, Stefania
dc.description.abstract: Logic has been proved useful to model various aspects of the reasoning process of agents and Multi-Agent Systems (MAS). In this paper, we report about a line of work carried on in cooperation with Andrea Formisano (former Eugenio’s Ph.D. student) and Valentina Pitoni, to explore some social aspects of such systems. The aim is to formally model (aspects of ) the group dynamics of cooperative agents. We have proposed a particular logical framework (the Logic of “Inferable” L-DINF), where a group of cooperative agents can jointly perform actions. I.e., at least one agent of the group can perform the action, either with the approval of the group or on behalf of the group. We have been able to take into consideration actions’ cost, and the preferences that each agent may have for what concerns performing each action. Our focus is on: (i) explainability, i.e., the syntax of our logic is especially devised to make it possible to transpose a proof into a natural language explanation, in the perspective of trustworthy Artificial Intelligence (AI); (ii) the capability to construct and execute joint plans within a group of agents; (iii) the formalization of aspects of the Theory of Mind, which is an important social-cognitive skill that involves the ability to attribute mental states, including emotions, desires, beliefs, and knowledge both one’s own and those of others, and to reason about the practical consequences of such mental states; this capability is very relevant when agents have to interact with humans, and in particular in robotic applications; (iv) connection between theory and practice, so as to make our logic actually usable by systems’ designers. In this paper, we summarize our past work and propose some discussions, possible extensions and considerations.
2021-01-01T00:00:00Z{CUDA}: Set constraints on GPUsDovier, AgostinoFormisano, AndreaPontelli, EnricoTardivo, Fabiohttps://www.openstarts.units.it/handle/10077/333102024-08-14T00:14:30Z2021-01-01T00:00:00Zdc.title: {CUDA}: Set constraints on GPUs
dc.contributor.author: Dovier, Agostino; Formisano, Andrea; Pontelli, Enrico; Tardivo, Fabio
dc.description.abstract: Set constraints have been introduced in declarative programming languages in the Nineties as a consequence of a broader research on programming with sets and on computable set theory. General Purpose Graphics Processing Units (GPUs), originally developed for graphical purposes (e.g., for high definition video games), emerged recently as a powerful and cheap parallel architecture, widely available in most desktops and laptops computers. This paper presents a constraint solver on set constraints and its parallel implementation on GPUs.
2021-01-01T00:00:00Z{log}: Set formulas as programsCristiá, MassimilianoRossi, Gianfrancohttps://www.openstarts.units.it/handle/10077/333092024-08-17T00:02:33Z2021-01-01T00:00:00Zdc.title: {log}: Set formulas as programs
dc.contributor.author: Cristiá, Massimiliano; Rossi, Gianfranco
dc.description.abstract: {log} is a programming language at the intersection of Constraint Logic Programming, set programming and declarative programming. But {log} is also a satisfiability solver for a theory of finite sets and finite binary relations. With {log} programmers can write abstract programs using all the power of set theory and binary relations. These programs are not very efficient but they are very close to specifications. Then, their correctness is more evident. Furthermore, {log} programs are also set formulas. Hence, programmers can use {log} again to automatically prove their programs verify non trivial properties. In this paper we show this development methodology by means of several examples.
2021-01-01T00:00:00Z