The main goal of the present paper is to extend classical results from the measure theory and dynamical systems to the fuzzy subset setting. In this paper, the notion of  dynamic equivalence relation is introduced and then it is proved that this relation is an equivalence relation. Also, a new metric on the collection of all equivalence classes is introduced and it is proved that this metric is...

The linear code equivalence problem is to decide whether two linear codes over Fq are identical up to a linear isometry of the Hamming space. The support splitting algorithm [25] runs in polynomial time for all but a negligible proportion of all linear codes, and solves the latter problem by recovering the isometry when it is just a permutation of the code support. While for a binary alphabet i...

In the paper, a complete system of transformation rules preserving the tree equivalence and a polynomial-time algorithm deciding the tree equivalence of linear polyadic recursion schemes are proposed. The algorithm is formulated as a sequential transformation process which brings together the schemes in question. In the last step, the tree equivalence problem for the given schemes is reduced to...

We consider the problem of checking equivalence of conjunctive queries with inequalities under bag (multiset) semantics. The problem is known to be decidable in pspace and as hard as graph isomorphism, but its exact complexity remains open. We introduce a natural restriction based on what we call the symmetry degree of queries, and show that when the symmetry degree is bounded by a fixed polyno...

We study the problem of properly learning unions of two axis parallel rectangles over the domain f n g in the on line model with equivalence queries When only O log n equivalence queries are allowed this problem is one of the ve interesting open problems proposed in regarding learning geometric concepts In this paper we design an e cient algorithm that properly learns unions of two rectangles o...

The linear code equivalence problem is to decide whether two linear codes over Fq are identical up to a linear isometry of the Hamming space. The support splitting algorithm [23] runs in polynomial time for all but a negligible proportion of all linear codes, and solves the latter problem by recovering the isometry when it is just a permutation of the code support. While for a binary alphabet i...

We consider the equivalence problem for labeled Markov chains (LMCs), where each state is labeled with an observation. Two LMCs are equivalent if every finite sequence of observations has the same probability of occurrence in the two LMCs. We show that equivalence can be decided in polynomial time, using a reduction to the equivalence problem for probabilistic automata, which is known to be sol...

An example is provided to show that the natural asymptotic equivalence does not hold between any pairs of three nonparametric experiments: density problem, white noise with drift and nonparametric regression, when the smoothness index of the unknown nonparametric function class is 1/2. 1. Introduction. There have recently been several papers demonstrating the global asymptotic equivalence of ce...

We present CONEQCT: a contextual equivalence checking tool for terms of IMJ∗, a fragment of Interface Middleweight Java for which the problem is decidable. Given two, possibly open (containing free identifiers), terms of the language, the contextual equivalence problem asks if the terms can be distinguished by any possible IMJ context. Although there has been a lot of prior work describing meth...

The code equivalence problem is to decide whether two linear codes over Fq are identical up to a linear isometry of the Hamming space. In this paper, we review the hardness of code equivalence over Fq due to some recent negative results and argue on the possible implications in code-based cryptography. In particular, we present an improved version of the three-pass identification scheme of Gira...