In this paper we study the ring of graph invariants, focusing mainly on the invariants of simple graphs. We show that all other invariants, such as sorted eigenvalues, degree sequences and canonical permutations, belong to this ring. In fact, every graph invariant is a linear combination of the basic graph invariants which we study in this paper. To prove that two graphs are isomorphic, a numbe...

We analyze the Matrix Berlekamp/Massey algorithm, which generalizes the Berlekamp/Massey algorithm [Massey 1969] for computing linear generators of scalar sequences. The Matrix Berlekamp/Massey algorithm computes a minimal matrix generator of a linearly generated matrix sequence and has been first introduced by [Rissanen 1972a], [Dickinson et al. 1974] and [Coppersmith 1994]. Our version of the...

In his celebrated paper on the algebraic structure of ConvoJutional codes, Forney 111 showed that by using the invariant-factor theorem, one can transform an arbitrary polynomial generator matrix for an (n, k ) convolutional code C into a basic (and ultimately a minimal) generator matrix for C. He also showed how to find a polynomial inverse for a basic generator matrix for C, and a basic gener...

We study the state complexity of regular operations in the class of ideal languages. A language L ⊆ Σ∗ is a right (left) ideal if it satisfies L = LΣ∗ (L = Σ∗L). It is a two-sided ideal if L = Σ∗LΣ∗, and an all-sided ideal if L = Σ∗ L, the shuffle of Σ∗ with L. We prefer the term “quotient complexity” instead of “state complexity”, and we use derivatives to calculate upper bounds on quotient co...

We present an efficient algorithm for computing the minimal trellis for a group code over a finite abelian group, given a generator matrix for the code. We also show how to compute a succinct representation of the minimal trellis for such a code, and present algorithms that use this information to compute efficiently local descriptions of the minimal trellis. This extends the work of Kschischan...

The problem of the relevance and the usefulness of extracted association rules is becoming of primary importance, since an overwhelming number of association rules may be derived even from reasonably sized databases. This requires the extraction of generic bases of association rules, of reduced size and which summarize the same information. Using the concept of minimal generator, we propose an ...

The problem of the relevance and the usefulness of extracted association rules is becoming of primary importance, since an overwhelming number of association rules may be derived, even from reasonably sized databases. To overcome such drawback, the extraction of reduced size generic bases of association rules seems to be promising. Using the concept of minimal generator, we propose an algorithm...

Understanding the generative mechanism of a natural system is a vital component of the scientific method. Here, we investigate one of the fundamental steps toward this goal by presenting the minimal generator of an arbitrary binary Markov process. This is a class of processes whose predictive model is well known. Surprisingly, the generative model requires three distinct topologies for differen...

It has previously been shown that the site of production of the generator potential in Pacinian corpuscles is the receptor membrane of the non-myelinated ending, and the site of initiation of the nerve impulse, the adjacent (first) Ranvier node. Effects of membrane polarization of these sites were studied in the present work. Nerve ending and first Ranvier node were isolated by dissection, elec...