We extend the regular model checking framework so that it can handle systems with arbitrary width tree-like structures. Configurations of a system are represented by trees of arbitrary arities, sets of configurations are represented by regular hedge automata, and the dynamics of a system is modeled by a regular hedge transducer. We consider the problem of computing the transitive closure T + of...

A bst ract. A one-dimensional cellular automaton rule with specified boundary conditions can be considered as acting simultaneously on all finite lattices, which gives a mapping between formal languages. Regular lang uages are always mapped to regular langu ages, contex t-free to context-free, context-sensitive to context-sensitive, and recursive sets to recursive sets . In particular, the fini...

A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional spacetimes, etc.), as well as rapidly-evolving systems. The technique employed is the Finite Element Method (FEM), which has been used to solve engineering struc...

The optimal stopping rules with multiple selections of m 1 objects with the objective of maximizing the probability of obtaining the best object are studied for two problems with an unknown number of objects:the problem with a random number of objects, and the problem where the objects arrive according to a homogeneous Poisson process with unknown intensity . These two problems are variation of...

A comprehensive graph theoretical and finite geometrical study of the commutation relations between the generalized Pauli operators of N -qudits is performed in which vertices/points correspond to the operators and edges/lines join commuting pairs of them. As per two-qubits, all basic properties and partitionings of the corresponding Pauli graph are embodied in the geometry of the generalized q...

This paper concerns power series of an arithmetic nature that arise in the analysis of divide-and-conquer algorithms. Two key notions are studied: that of B-regular sequence and that of Mahlerian sequence with their associated power series. Firstly we emphasize the link between rational series over the alphabet fx0;x1;:::;xB?1g and B-regular series. Secondly we extend the theorem of Christol, K...

A new fast multipole formulation for solving elliptic difference equations on unbounded domains and its parallel implementation are presented. These difference equations can arise directly in the description of physical systems, e.g. crystal structures, or indirectly through the discretization of PDEs. In the analog to solving continuous inhomogeneous differential equations using Green’s functi...

We propose new solutions to ultradiscrete Painlevé equations that cannot be derived using the ultradiscretization method. In particular, we show the third ultradiscrete Painelevé equation possesses hypergeometric solutions. We show this by considering a lift of these equations to a non-archimedean valuation field in which we may relax the subtraction free framework of previous explorations of t...