Internship proposal Graph and Automata Algorithms for Verification

Graph and automata theory are widely used in the algorithmic solution of fundamental problems in verification. Verification problems often boil down to solving reachability questions in graphs, optimization problems, and combinatorial problems in automata. Fundamental algorithmic problems in computer science have been well studied, such as the shortest path problem, the travelling salesman problem, etc. A similar classical problem in discrete planning is the finite-horizon planning problem [2], where the input is a directed graph with weights assigned to every edge and a time horizon T , and the goal is to find a path of length T that maximizes the total utility defined as the sum of the weights of the path. This computational problem for finite-horizon planning has applications in artificial intelligence and robotics [4, Chapter 10, Chapter 25], as well as in control theory and game theory [1, Chapter 2.2], [3, Chapter 6]. In this internship (with possible continuation as a phd thesis), we consider relaxations of the finite-horizon problem where the original question with a fixed horizon T is replaced by an expected time horizon, either given through a fixed stopping-time distribution, or through an adversarial distribution where the stopping-time distribution is unknown and decided by an adversary. We are looking for algorithmic solutions and structural properties in the case of graphs, as well as in more powerful models such as Markov processes, pushdown graphs, and timed systems. Several theoretical questions can be investigated and the solutions and heuristics can possibly lead to prototype implementations.