Ph.D XL

Supervisor: Alberto Policriti

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Mail: boscaratto.simone@spes.uniud.it

Research Project

Fundamental properties of an Ackermann-like encoding of hereditarily finite sets, hypersets and multisets

My research project focuses on a real-valued variant of the Ackermann encoding of hereditarily finite sets, which can also be extended to hereditarily finite rational hypersets – characterised by loops in the membership chains, so that a hyperset can belong to itself – and hereditarily finite multisets – allowing multiple occurrences of the same set at any nesting depth.

This study has as main objectives to prove that a map within this encoding scheme uniquely assigns a real non-negative number to each member of these families of such extended notions of set, and that it is an injective map with respect to its codomain. This could have quite relevant consequences on declarative programming, where sets and their generalisations play a prominent role.

Assigning codes to (hyper-, multi-) sets, which can be translated into giving a number to each node of a graph, can help tackling the graph isomorphism problem. On the other hand, it can be applied to minimise deterministic finite automata (DFA), which is equivalent to find the coarsest stable partition of the set of nodes of a graph.