Related papers: On the equivalence of two quantifier elimination t…

We introduce two new model comparison games that characterize separability by first-order formulas with generalized quantifiers. One is built on the Ehrenfeucht-Fra\"iss\'e game and the other is a formula-size game.

In this paper we develop a novel bootstrap test for the comparison of two multinomial distributions. The two distributions are called {\it equivalent} or {\it similar} if a norm of the difference between the class probabilities is smaller…

We establish the strictness of several set quantifier alternation hierarchies that are based on modal logic, evaluated on various classes of finite graphs. This extends to the modal setting a celebrated result of Matz, Schweikardt and…

Types over a discrete valued field $(K,v)$ are computational objects that parameterize certain families of monic irreducible polynomials in $K_v[x]$, where $K_v$ is the completion of $K$ at $v$. Two types are considered to be equivalent if…

A Basarab-Kuhlmann style language L_RV is introduced in the Hrushovski-Kazhdan integration theory. The theory ACVF of algebraically closed valued fields formulated in this language admits quantifier elimination. In this paper, using…

A notion of generalized quantifier in computational complexity theory is explored and used to give a unified treatment of leaf language definability, oracle separations, type 2 operators, and circuits with monoidal gates. Relations to…

This article is concerned with measure equivalence and uniform measure equivalence of locally compact, second countable groups. We show that two unimodular, locally compact, second countable groups are measure equivalent if and only if they…

The study of computability has its origin in Hilbert's conference of 1900, where an adjacent question, to the ones he asked, is to give a precise description of the notion of algorithm. In the search for a good definition arose three…

Let $A$ and $B$ be Gorenstein Artin algebras of Cohen-Macaulay finite type. We prove that, if $A$ and $B$ are derived equivalent, then their Cohen-Macaulay Auslander algebras are also derived equivalent.

In this paper, we present a much simpler, direct and elegant approach to the equivalence problem of {\it measure many one-way quantum finite automata} (MM-1QFAs). The approach is essentially generalized from the work of Carlyle [J. Math.…

The minimal deterministic finite automaton is generally used to determine regular languages equality. Antimirov and Mosses proposed a rewrite system for deciding regular expressions equivalence of which Almeida et al. presented an improved…

This paper presents a type theory with a form of equality reflection: provable equalities can be used to coerce the type of a term. Coercions and other annotations, including implicit arguments, are dropped during reduction of terms. We…

While many different models for $(\infty,1)$-categories are currently being used, it is known that they are Quillen equivalent to one another. Several higher-order analogues of them are being developed as models for $(\infty,…

We establish relative quantifier elimination for valued fields of residue characteristic zero enriched with a non-surjective valued field endomorphism, building on recent work of Dor and Halevi. In particular, we deduce relative quantifier…

K. He, J. Hou, and M. Li have recently given a sufficient and necessary condition for unitary equivalence of quantum states. This condition is based on the von Neumann entropy. In this note we first give a short proof of their result, and…

This note proves that, as K-theory elements, the symbol classes of the de Rham operator and the signature operator on a closed manifold of even dimension are congruent mod 2. An equivariant generalization is given pertaining to the…

In this paper, we consider the problem of model equivalence for quantum systems. Two models are said to be (input-output) equivalent if they give the same output for every admissible input. In the case of quantum systems, the output is the…

In this paper, we study a positive characteristic analogue of the centers of log canonicity of a pair $(R, \Delta)$. We call these analogues centers of $F$-purity. We prove positive characteristic analogues of subadjunction-like results,…

We examine an equivalence relation between free homotopy classes of closed curves on the pair of pants known as k-equivalence, a generalization of a concept previously defined by Leininger. We prove that two classes of closed curves on the…

A recently proposed test of quantumness [R. Alicki and N. Van Ryn, J. Phys. A: Math. Theor. 41 062001 (2008)] is put into a broader mathematical and physical perspective. The notion of quantumness witness is introduced, in analogy to…