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The recently proven Quantum Lovasz Local Lemma generalises the well-known Lovasz Local Lemma. It states that, if a collection of subspace constraints are "weakly dependent", there necessarily exists a state satisfying all constraints. It…
The Lov\'{a}sz Local Lemma is a very powerful tool in probabilistic combinatorics, that is often used to prove existence of combinatorial objects satisfying certain constraints. Moser and Tardos have shown that the LLL gives more than just…
In this paper a new mathematical procedure is presented for combining different pieces of evidence which are represented in the interval form to reflect our knowledge about the truth of a hypothesis. Evidences may be correlated to each…
In this note let us give two remarks on proof-theory of PA. First a derivability relation is introduced to bound witnesses for provable $\Sigma_{1}$-formulas in PA. Second Paris-Harrington's proof for their independence result is…
We apply the bound on independence number via Lov{\'a}sz theta function to eventown problem and its generalizations over $\mathbb{Z}_n$.
We uncover a close relationship between combinatorial and syntactic proofs for first-order logic (without equality). Whereas syntactic proofs are formalized in a deductive proof system based on inference rules, a combinatorial proof is a…
The Lov\'asz Local Lemma is a versatile result in probability theory, characterizing circumstances in which a collection of $n$ `bad events', each occurring with probability at most $p$ and dependent on a set of underlying random variables,…
A paper of the first author and Zilke proposed seven combinatorial problems around formulas for the characteristic polynomial and the exponents of an isolated quasihomogeneous singularity. The most important of them was a conjecture on the…
We introduce an algorithm that exploits a combinatorial symmetry of an arrangement in order to produce a geometric reflection between two disconnected components of its moduli space. We apply this method to disqualify three real examples…
Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…
The lefthanded Lov\'asz local lemma (LLLL) is a generalization of the Lov\'asz local lemma (LLL), a powerful technique from the probabilistic method. We prove a computable version of the LLLL and use it to effectivize a collection of…
We investigate the notion of independence, which is at the basis of many, seemingly unrelated, properties of logic like Rational Monotony in non-monotonic logics, and interpolation theorems.
Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…
Let $P$ be a finite poset with an element $s$ such that (1) for all $x\in P$, either $s\vee x$ or $s\wedge x$ exists; and (2) for all $x,y\in P$ such that $x<y$, if $s\wedge x$ does not exist but $s\wedge y$ does exist, then $(s\wedge…
Recently P. Wocjan and M. Horodecki [quant-ph/0503129] gave a characterization of combinatorially independent permutation separability criteria. Combinatorial independence is a necessary condition for permutations to yield truly independent…
This paper presents an approach to lemma synthesis to support advanced inductive entailment procedures based on separation logic. We first propose a mechanism where lemmas are automatically proven and systematically applied. The lemmas may…
In this note, we show how a combinatorial identity of Frisch can be applied to prove and generalize some well-known identities involving harmonic numbers. We also present some combinatorial identities involving odd harmonic numbers which…
For years, independence has been considered as an important concept in many disciplines. Nevertheless, we present the first research that investigates the discovery problem of independence in data. In its arguably simplest form,…
We consider the recent formulation of the Algorithmic Lov\'asz Local Lemma [10,2,3] for finding objects that avoid `bad features', or `flaws'. It extends the Moser-Tardos resampling algorithm [17] to more general discrete spaces. At each…
We introduce an atomic formula intuitively saying that given variables are independent from given other variables if a third set of variables is kept constant. We contrast this with dependence logic. We show that our independence atom gives…