Daniele Nantes on Estruturas Formais, Fundamentos e Aplicações

Topological graphs and the Four Color Theorem

Fri, 07 Jun 2019 14:30:00 -0300

$\lambda$-terms can be syntactically represented in different ways than the usual term strings; for example, one can use combinators, string diagrams and for the linear case Zeilberger’s trivalent maps. The main purpose of this paper is to study the relation between arbitrary $\lambda$-terms and maps over orientable surfaces contained in $\mathbb{R}^3$. For this reason, topological graphs are introduced. These graphs include free-edges and hyper-edges to represent, respectively, free and multiple occurrences of variables. Arbitrary $\lambda$-terms without clashes are represented by a subclass of these graphs, called $\omega$-graphs, that include trivalent maps. A translation from $\lambda$-terms into topological graphs is given. The converse of the translation provides a decomposition algorithm that outputs a $\lambda$-term in the class of $\alpha$-equivalent terms associated to each topological graph given as input. This translation provides different names for free-variables. As an application in graph theory, a version of the Four Color Theorem for $\omega$-graphs, which are not necessarily planar, is presented extending in this manner a previous result restricted to a subclass of trivalent maps.

Relating Process Languages for Security and Communication Correctness

Wed, 02 May 2018 14:30:00 -0300

Process calculi are expressive specification languages for concurrency. They have been very successful in two research strands:

the analysis of security protocols and
the enforcement of correct message-passing programs.

Despite their shared foundations, languages and reasoning techniques for (1) and (2) have been separately developed.

Here we connect two representative calculi from (1) and (2): we encode a (high-level) pi-calculus for multiparty sessions into a (low-level) applied pi-calculus for security protocols. We establish the correctness of our encoding, and we show how it enables the integrated analysis of security properties and communication correctness by re-using existing tools

Daniele Nantes

Mon, 01 Jan 0001 00:00:00 +0000

Sua pesquisa, em área de fronteira, engloba técnicas matemática e computacionais, bem como suas aplicações em segurança de protocolos criptográficos. Dentre suas áreas de interesse estão: Teoria da Computação, Lógica Formal, Teoria da Complexidade, Teoria da Reescrita, Lógica Nominal, Pi-Calculus e Criptografia.