Validity-Guided Synthesis of Reactive Systems from Assume-Guarantee Contracts

Automated synthesis of reactive systems from specifications has been a topic of research for decades. Recently, a variety of approaches have been proposed to extend synthesis of reactive systems from proposi- tional specifications towards specifications over rich theories. We propose a novel, completely automated approach to program synthesis which reduces the problem to deciding the validity of a set of forall-exists formulas. In spirit of IC3 / PDR, our problem space is recursively refined by blocking out regions of unsafe states, aiming to discover a fixpoint that describes safe reactions. If such a fixpoint is found, we construct a witness that is directly translated into an implementation. We implemented the algorithm on top of the JKind model checker, and exercised it against contracts written using the Lustre specification language. Experimental results show how the new algorithm outperforms JKinds already existing synthesis procedure based on k-induction and addresses soundness issues in the k-inductive approach with respect to unrealizable results.Comment: 18 pages, 5 figures, 2 table

Patrolling a path connecting a set of points with unbalanced frequencies of visits

Patrolling consists of scheduling perpetual movements of a collection of mobile robots, so that each point of the environment is regularly revisited by any robot in the collection. In previous research, it was assumed that all points of the environment needed to be revisited with the same minimal frequency. In this paper we study efficient patrolling protocols for points located on a path, where each point may have a different constraint on frequency of visits. The problem of visiting such divergent points was recently posed by Gąsieniec et al. in [14], where the authors study protocols using a single robot patrolling a set of n points located in nodes of a complete graph and in Euclidean spaces. The focus in this paper is on patrolling with two robots. We adopt a scenario in which all points to be patrolled are located on a line. We provide several approximation algorithms concluding with the best currently known 3 -approximation

The Cinderella game on holes and anti-holes

We investigate a two-player game on graphs, where one player (Cinderella) wants to keep the behavior of an underlying water-bucket system stable whereas the other player (the wicked Stepmother) wants to cause overflows. The bucket number of a graph G is the smallest possible bucket size with which Cinderella can win the game. We determine the bucket numbers of all perfect graphs, and we also derive results on the bucket numbers of certain non-perfect graphs. In particular, we analyze the game on holes and (partially) on anti-holes for the cases where Cinderella sticks to a simple greedy strategy