We study the min-max problem in factor graphs, which seeks the assignment that minimizes the maximum value over all factors. We reduce this problem to both min-sum and sum-product inference, and focus on the later. This approach reduces the min-max inference problem to a sequence of constraint satisfaction problems (CSPs) which allows us to sample from a uniform distribution over the set of sol...

Brüggemann-Klein and Wood define a one-unambiguous regular language as a language that can be recognized by a deterministic Glushkov automaton. They give a procedure performed on the minimal DFA, the BW-test, to decide whether a language is one-unambiguous. Block determinism is an extension of one-unambiguity while considering non-empty words as symbols and prefix-freeness as determinism. A blo...

This paper considers the k-set agreement problem in a crash-prone asynchronous message passing system enriched with failure detectors. Two classes of failure detectors have been previously identified as necessary to solve asynchronous k-set agreement: the class anti-leader anti−Ω and the weak-quorum class Σk. The paper investigates the families of failure detector (anti−Ωx)1≤x≤n and (Σz)1≤z≤n. ...

In this paper we consider a synchronous message passing system in which in every round an external adversary is able to send each processor up to k messages with falsified sender identities and arbitrary content. It is formally shown that this impersonation model is slightly stronger than the asynchronous message passing model with crash failures. In particular, we prove that (k+1)-set agreemen...

It is proved that for any given integer k > 2 and a k-monotone function g, there exists a k-monotone function g̃ ≤ g of the form c(a − x) + and passing through a fixed point in the support of g. The result is motivated by the problem of the existence of the LSE of a k-monotone density.

Let K be a field, S a polynomial ring and E an exterior algebra over K, both in a finite set of variables. We study rigidity properties of the graded Betti numbers of graded ideals in S and E when passing to their generic initial ideals. First, we prove that if the graded Betti numbers β ii+k(S/I) = β S ii+k (

Graphical models use the intuitive and well-studied methods of graph theory to implicitly represent dependencies between variables in large systems. They can model the global behaviour of a complex system by specifying only local factors.This thesis studies inference in discrete graphical models from an “algebraic perspective” and the ways inference can be used to express and approximate NP-har...

For a variety X of dimension n in Pr, r n(k + 1) + k, the kth secant order of X is the number μk(X) of (k + 1)-secant k-spaces passing through a general point of the kth secant variety. We show that, if r > n(k + 1) + k, then μk(X) = 1 unless X is k-weakly defective. Furthermore we give a complete classification of surfaces X ⊂ Pr, r > 3k + 2, for which μk(X) > 1.

In the k-set agreement problem, each processor starts with a private input value and eventually decides on an output value. At most k distinct output values may be chosen, and every processor’s output value must be one of the proposed values. We consider a synchronous message passing system, and we prove a tight bound of f/k +2 rounds of communication for all processors to decide in every run i...