Finite state automata with counters are useful for modeling systems with discrete parameters. The calculation of state invariants is an important tool in the analysis of such systems. Previous authors have presented techniques for the calculation of state invariants based on their approximation by convex polyhedra. In this paper we present a new method for the calculation of invariants for nite...

We present a dynamic programming approach for the solution of first-order Markov decisions processes. This technique uses an MDP whose dynamics is represented in a variant of the situation calculus allowing for stochastic actions. It produces a logical description of the optimal value function and policy by constructing a set of first-order formulae that minimally partition state space accordin...

Symbolic preprocessing techniques are very useful to obtain low order LFT-representations for parametric models. In this paper we give an overview about existing preprocessing methods and we present new techniques and enhancements of existing methods. All methods are implemented in the new version 2 of the LFR-toolbox and their capabilities are illustrated by a challenging aircraft parametric u...

Tree theory, partitions of integer numbers, combinatorial mathematics and computer algebra are the basis for the construction of a powerful and efficient symbolic package for the derivation of Runge Kutta order conditions and principal truncation error terms.

The singularity structure of a second-order ordinary differential equation with polynomial coefficients often yields the type solution. It is shown that $\theta$-operator method can be used as symbolic computational approach to obtain indicial and recurrence relation. Consequently, leads transformations yield solution in terms special function, if suitable. Hypergeometric Heun-type equations ar...

The data descriptions of the units are called "symbolic" when they are more complex than standard ones due to the fact that they contain internal variation and are structured. Symbolic data arise from many sources, for instance in order to summarise huge Relational Data Bases by their underlying concepts. "Extracting knowledge" means getting explanatory results, that why, "symbolic objects" are...