Nominal C-Unification

Nominal unification is an extension of first-order unification that takes into account the \alpha-equivalence relation generated by binding operators, following the nominal approach. We propose a sound and complete procedure for nominal unification with commutative operators, or nominal C-unification for short, which has been formalised in Coq. The procedure transforms nominal C-unification problems into simpler (finite families) of fixpoint problems, whose solutions can be generated by algebraic techniques on combinatorics of permutations.Comment: Pre-proceedings paper presented at the 27th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur, Belgium, 10-12 October 2017 (arXiv:1708.07854

On P-transitive graphs and applications

We introduce a new class of graphs which we call P-transitive graphs, lying between transitive and 3-transitive graphs. First we show that the analogue of de Jongh-Sambin Theorem is false for wellfounded P-transitive graphs; then we show that the mu-calculus fixpoint hierarchy is infinite for P-transitive graphs. Both results contrast with the case of transitive graphs. We give also an undecidability result for an enriched mu-calculus on P-transitive graphs. Finally, we consider a polynomial time reduction from the model checking problem on arbitrary graphs to the model checking problem on P-transitive graphs. All these results carry over to 3-transitive graphs.Comment: In Proceedings GandALF 2011, arXiv:1106.081

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science

On-board Trajectory Computation for Mars Atmospheric Entry Based on Parametric Sensitivity Analysis of Optimal Control Problems

This thesis develops a precision guidance algorithm for the entry of a small capsule into the atmosphere of Mars. The entry problem is treated as nonlinear optimal control problem and the thesis focuses on developing a suboptimal feedback law. Therefore parametric sensitivity analysis of optimal control problems is combined with dynamic programming. This approach enables a real-time capable, locally suboptimal feedback scheme. The optimal control problem is initially considered in open loop fashion. To synthesize the feedback law, the optimal control problem is embedded into a family of neighboring problems, which are described by a parameter vector. The optimal solution for a nominal set of parameters is determined using direct optimization methods. In addition the directional derivatives (sensitivities) of the optimal solution with respect to the parameters are computed. Knowledge of the nominal solution and the sensitivities allows, under certain conditions, to apply Taylor series expansion to approximate the optimal solution for disturbed parameters almost instantly. Additional correction steps can be applied to improve the optimality of the solution and to eliminate errors in the constraints. To transfer this strategy to the closed loop system, the computation of the sensitivities is performed with respect to different initial conditions. Determining the perturbation direction and interpolating between sensitivities of neighboring initial conditions allows the approximation of the extremal field in a neighborhood of the nominal trajectory. This constitutes a locally suboptimal feedback law. The proposed strategy is applied to the atmospheric entry problem. The developed algorithm is part of the main control loop, i.e. optimal controls and trajectories are computed at a fixed rate, taking into account the current state and parameters. This approach is combined with a trajectory tracking controller based on the aerodynamic drag. The performance and the strengthsa and weaknesses of this two degree of freedom guidance system are analyzed using Monte Carlo simulation. Finally the real-time capability of the proposed algorithm is demonstrated in a flight representative processor-in-the-loop environment