Let G be a finite group. We classify G-equivariant flow equivalence of nontrivial irreducible shifts of finite type in terms of (i) elementary equivalence of matrices over ZG and (ii) the conjugacy class in ZG of the group of G-weights of cycles based at a fixed vertex. In the case G = Z/2, we have the classification for twistwise flow equivalence. We include some algebraic results and examples...

We introduce Brauer complex of symmetric SB-algebra, and reformulate in terms of Brauer complex the so far known invariants of stable and derived equivalence of symmetric SB-algebras. In particular, the genus of Brauer complex turns out to be invariant under derived equivalence. We study transformations of Brauer complexes which preserve class of derived equivalence. Additionally, we establish ...

Spirtes, Glymour and Scheines [Causation, Prediction, and Search (1993) Springer] described a pointwise consistent estimator of the Markov equivalence class of any causal structure that can be represented by a directed acyclic graph for any parametric family with a uniformly consistent test of conditional independence, under the Causal Markov and Causal Faithfulness assumptions. Robins et al. [...

In this paper, we provide a behavioural characterization of the class of finite, seriesparallel pomsets by showing that this simple model based on partial orders is fullyabstract with respect to the behavioural equivalence obtained by applying Abramsky's testing scenario for bisimulation equivalence, [Ab87], in all refinement contexts, [AH89]. This casts the observability of series-parallel por...

We prove, in ZF+Σ2-determinacy, that for any analytic equivalence relation E, the following three statements are equivalent: (1) E does not have perfectly many classes, (2) E satisfies hyperarithmetic-is-recursive on a cone, and (3) relative to some oracle, for every equivalence class [Y ]E we have that a real X computes a member of the equivalence class if and only if ω 1 ≥ ω [Y ] 1 . We also ...

Parikh matrices have been a powerful tool in arithmetizing words by numerical quantities. However, the dependence on the ordering of the alphabet is inherited by Parikh matrices. Strong M -equivalence is proposed as a canonical alternative to M -equivalence to get rid of this undesirable property. Some characterization of strong M -equivalence for a restricted class of words is obtained. Finall...

A stimulus class can be composed of perceptually different but functionally equivalent stimuli. The relations between the stimuli that are grouped in a class can be learned or derived from other stimulus relations. If stimulus A is equivalent to B, and B is equivalent to C, then the equivalence between A and C can be derived without explicit training. In this work we propose, with a neurocomput...

We study the NFA reductions by invariant equivalences. It is well-known that the NFA minimization problem is PSPACE-complete. Therefore, there have been approaches to reduce the size of NFAs in low polynomial time by computing invariant equivalence and merging the states within same equivalence class. Here we consider the nondeterminism reduction of NFAs by invariant equivalences. We, in partic...

Functional equivalence of radial basis function (RBF) networks and a class of fuzzy inference systems is considered. The class of fuuy systems based on the Takagi-Sugeno model is referred to as TS-model of fuzzy inference. From the abstract mathematical viewpoint the functional equivalence between radial basis function networks and fuzzy inference systems is already shown. However, from the vie...

We develop a general framework for the study of strong Morita equivalence in which C∗algebras and hermitian star products on Poisson manifolds are treated in equal footing. We compare strong and ring-theoretic Morita equivalences in terms of their Picard groupoids for a certain class of unital ∗-algebras encompassing both examples. Within this class, we show that both notions of Morita equivale...