Decidability in the logic of subsequences and supersequences

We consider first-order logics of sequences ordered by the subsequence ordering, aka sequence embedding. We show that the \Sigma_2 theory is undecidable, answering a question left open by Kuske. Regarding fragments with a bounded number of variables, we show that the FO2 theory is decidable while the FO3 theory is undecidable

On Functions Weakly Computable by Pushdown Petri Nets and Related Systems

We consider numerical functions weakly computable by grammar-controlled vector addition systems (GVASes, a variant of pushdown Petri nets). GVASes can weakly compute all fast growing functions $F_\alpha$ for $\alpha<\omega^\omega$, hence they are computationally more powerful than standard vector addition systems. On the other hand they cannot weakly compute the inverses $F_\alpha^{-1}$ or indeed any sublinear function. The proof relies on a pumping lemma for runs of GVASes that is of independent interest

Complexity Hierarchies Beyond Elementary

We introduce a hierarchy of fast-growing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a non-elementary complexity, which occur naturally in logic, combinatorics, formal languages, verification, etc., with complexities ranging from simple towers of exponentials to Ackermannian and beyond.Comment: Version 3 is the published version in TOCT 8(1:3), 2016. I will keep updating the catalogue of problems from Section 6 in future revision

The Cayley-graph of the queue monoid: logic and decidability

We investigate the decidability of logical aspects of graphs that arise as Cayley-graphs of the so-called queue monoids. These monoids model the behavior of the classical (reliable) fifo-queues. We answer a question raised by Huschenbett, Kuske, and Zetzsche and prove the decidability of the first-order theory of these graphs with the help of an - at least for the authors - new combination of the well-known method from Ferrante and Rackoff and an automata-based approach. On the other hand, we prove that the monadic second-order of the queue monoid's Cayley-graph is undecidable

The complexity of coverability in ν-Petri nets

We show that the coverability problem in ν-Petri nets is complete for ‘double Ackermann’ time, thus closing an open complexity gap between an Ackermann lower bound and a hyper-Ackermann upper bound. The coverability problem captures the verification of safety properties in this nominal extension of Petri nets with name management and fresh name creation. Our completeness result establishes ν-Petri nets as a model of intermediate power among the formalisms of nets enriched with data, and relies on new algorithmic insights brought by the use of well-quasi-order ideals

Reachability problems on reliable and lossy queue automata

We study the reachability problem for queue automata and lossy queue automata. Concretely, we consider the set of queue contents which are forwards resp. backwards reachable from a given set of queue contents. Here, we prove the preservation of regularity if the queue automaton loops through some special sets of transformation sequences. This is a generalization of the results by Boigelot et al. and Abdulla et al. regarding queue automata looping through a single sequence of transformations. We also prove that our construction is possible in polynomial time

On Functions Weakly Computable by Pushdown Petri Nets and Related Systems

We consider numerical functions weakly computable by grammar-controlled vector addition systems (GVASes, a variant of pushdown Petri nets). GVASes can weakly compute all fast growing functions $F_\alpha$ for $\alpha<\omega^\omega$, hence they are computationally more powerful than standard vector addition systems. On the other hand they cannot weakly compute the inverses $F_\alpha^{-1}$ or indeed any sublinear function. The proof relies on a pumping lemma for runs of GVASes that is of independent interest