The role played by continuous morphisms in propositional modal logic is investigated: it turns out that they are strictly related to filtrations and to suitable variants of the notion of a free algebra. We also employ continuous morphisms in the incremental construction of (standard) finitely generated free S4-algebras. This Technical Report reproduces the content of my talk given at the worksh...

The paper approaches the classical combinatorial problem of freeness of words, in the more general case of partial words. First, we propose an algorithm that tests efficiently whether a partial word is kfree or not. Then, we show that there exist arbitrarily many cube-free infinite partial words containing an infinite number of holes, over binary alphabets; thus, there exist arbitrarily many k-...

Let M be a B-probability space. Assume that B itself is a D-probability space; then M can be viewed as D-probability space as well. Let X ∈ M. We look at the question of relating the properties of X as B-valued random variable to its properties as D-valued random variable. We characterize freeness of X from B with amalgamation over D: (a) in terms of a certain fac-torization condition linking t...

In this paper we propose a new type of “image” representation for periodic behaviors and analyze the relationship between image representability and controllability, showing that the correspondence, which exists in the time-invariant case, generalizes to periodic behaviors. We also show that the concept of free variable used in the time-invariant case cannot be transposed to the periodic case i...

I analyze an economy with uncertainty in which a set of indivisible objects and a certain amount of money is to be distributed among agents. The set of intertemporally fair social choice functions based on envy-freeness and Pareto efficiency is characterized. I give a necessary and sufficient condition for its non-emptiness and propose a mechanism that implements the set of intertemporally fair...

In this paper we define a property for multi-party protocols called exclusion-freeness. In multi-party protocols respecting the strongest definition of this property, participants are sure that they will not be excluded from a protocol’s execution and, consequently, they do not have to trust each other any more. We study this property on a wellknown multi-party fair exchange protocol with an on...

• Generalization of bipartiteness testing: " general graph partition properties " (GGPT) • Testing-freeness via regularity: – Szemerédi Regularity Lemma (SRL) –-removal lemma (tester with query complexity O (1), with the dependence on is a tower of 1.2 Today • Quick sketch of the proof of SRL • 1 Ω(log 1) lower bound for 1-sided error testers for-freeness (ruling out poly(1)-query testers) • Bo...

The auction scheme that provides receipt-freeness, prevents the bidders from bid-rigging by the coercers. Bid-rigging is a dangerous attack in electronic auction. This happen if the bidder gets a receipt of his bidding price, which proves his bidding prices, from the auction protocol. The coercers used to force the bidders to disclose their receipts and hence bidders lose the secrecy of their b...

We show that Terao's Conjecture ("Freeness of the module of logarithmic forms at a hyperplane arrangement is determined by its abstract matroid") holds over fields with at most four elements. However, an example demonstrates that the field characteristic has to be fixed for this. 1. Free arrangements The present study continues an investigation of the connection between algebraic and combinator...

In this note we demonstrate an equivalent condition for bi-freeness, inspired by the well-known “vanishing of alternating centred moments” condition from free probability. We show that all products satisfying a centred condition on maximal monochromatic χ-intervals have vanishing moments if and only if the family of pairs of faces they come from is bi-free. In addition, we construct a bi-free u...