Multiset rewriting over Fibonacci and Tribonacci numbers

Determinantal Representations for Generalized Fibonacci and Tribonacci Numbers

the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Using certain Hessenberg matrices, we provide some determinantal representations of the general terms of second-and third-order linear recurrence sequences with arbitrary initial values. Moreover, we provide explicit formu...

Multiset rewriting by multiset onstraint solving

Constrained Multiset Rewriting

We investigate model checking of a computation model called Constrained Multiset Rewriting Systems (CMRS). A CMRS operates on configurations which are multisets of monadic predicate symbols, each with an argument ranging over the natural numbers. The transition relation is defined by a finite set of rewriting rules which are conditioned by simple inequalities on variables and constants. This mo...

Modular Multiset Rewriting

Rule-based languages are being used for ever more ambitious applications. As program size grows however, so does the overhead of team-based development, reusing components, and just keeping a large flat collection of rules from interfering. In this paper, we propose a module system for a small logicallymotivated rule-based language. The resulting modules are nothing more than rewrite rules of a...

Energy of Graphs, Matroids and Fibonacci Numbers

The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. In this article we consider the problem whether generalized Fibonacci constants $varphi_n$ $(ngeq 2)$ can be the energy of graphs. We show that $varphi_n$ cannot be the energy of graphs. Also we prove that all natural powers of $varphi_{2n}$ cannot be the energy of a matroid.