Sylvain Schmitz

Well-structured transition systems (WSTS) are an abstract family of systems that encompasses a vast landscape of infinite-state systems. By requiring a well-quasi-ordering (wqo) on the set of states, a WSTS enables generic algorithms for classic verification tasks such as coverability and termination. However, even for systems that are WSTS like vector addition systems (VAS), the framework is notoriously ill-equipped to analyse reachability (as opposed to coverability). Moreover, some important types of infinite-state systems fall out of WSTS' scope entirely, such as pushdown systems (PDS). Inspired by recent algorithmic techniques on VAS, we propose an abstract notion of systems where the set of runs is equipped with a wqo and supports amalgamation of runs. We show that it subsumes a large class of infinite-state systems, including (reachability languages of) VAS and PDS, and even all systems from the abstract framework of valence systems, except for those already known to be Turing-complete. Moreover, this abstract setting enables simple and general algorithmic solutions to unboundedness problems, which have received much attention in recent years. We present algorithms for the (i) simultaneous unboundedness problem (which implies computability of downward closures and decidability of separability by piecewise testable languages), (ii) computing priority downward closures, (iii) deciding whether a language is bounded, meaning included in w_l^* ··· w_k^* for some words w_l, …, w_k, and (iv) effective regularity of unary languages. This leads to either drastically simpler proofs or new decidability results for a rich variety of systems.

We show that provability in the implicational fragment of relevance logic is complete for doubly exponential time, using reductions to and from coverability in branching vector addition systems.

We study the complexity of reachability problems on branching extensions of vector addition systems, which allows us to derive new non-elementary complexity bounds for fragments and variants of propositional linear logic. We show that provability in the multiplicative exponential fragment is Tower-hard already in the affine case -- and hence non-elementary. We match this lower bound for the full propositional affine linear logic, proving its Tower-completeness. We also show that provability in propositional contractive linear logic is Ackermann-complete.

We generalise the hyperplane separation technique (Chatterjee and Velner, 2013) from multi-dimensional mean-payoff to energy games, and achieve an algorithm for solving the latter whose running time is exponential only in the dimension, but not in the number of vertices of the game graph. This answers an open question whether energy games with arbitrary initial credit can be solved in pseudo-polynomial time for fixed dimensions 3 or larger (Chaloupka, 2013). It also improves the complexity of solving multi-dimensional energy games with given initial credit from non-elementary (Br\'azdil, Jan\v{c}ar, and Ku\v{c}era, 2010) to 2EXPTIME, thus establishing their 2EXPTIME-completeness.

The reachability problem in vector addition systems is a central question, not only for the static verification of these systems, but also for many inter-reducible decision problems occurring in various fields. The currently best known upper bound on this problem is not primitive-recursive, even when considering systems of fixed dimension. We provide significant refinements to the classical decomposition algorithm of Mayr, Kosaraju, and Lambert and to its termination proof, which yield an ACKERMANN upper bound in the general case, and primitive-recursive upper bounds in fixed dimension. While this does not match the currently best known TOWER lower bound for reachability, it is optimal for related problems.

Checking whether two pushdown automata with restricted silent actions are weakly bisimilar was shown decidable by Sénizergues (1998, 2005). We provide the first known complexity upper bound for this famous problem, in the equivalent setting of first-order grammars. This ACKERMANN upper bound is optimal, and we also show that strong bisimilarity is primitive-recursive when the number of states of the automata is fixed.

Diagnosability and opacity are two well-studied problems in discrete-event systems. We revisit these two problems with respect to expressiveness and complexity issues. We first relate different notions of diagnosability and opacity. We consider in pa