Editors: Jan Friso Groote, Kim Guldstrand Larsen

Edge-coloured directed graphs provide an essential structure for modelling and analysis of complex systems arising in many scientific disciplines (e.g. feature-oriented systems, gene regulatory networks, etc.). One of the fundamental problems for edge-coloured graphs is the detection of strongly connected components, or SCCs. The size of edge-coloured graphs appearing in practice can be enormous both in the number of vertices and colours. The large number of vertices prevents us from analysing such graphs using explicit SCC detection algorithms, such as Tarjan's, which motivates the use of a symbolic approach. However, the large number of colours also renders existing symbolic SCC detection algorithms impractical. This paper proposes a novel algorithm that symbolically computes all the monochromatic strongly connected components of an edge-coloured graph. In the worst case, the algorithm performs $O(p \cdot n \cdot log~n)$ symbolic steps, where $p$ is the number of colours and $n$ is the number of vertices. We evaluate the algorithm using an experimental implementation based on binary decision diagrams (BDDs). Specifically, we use our implementation to explore the SCCs of a large collection of coloured graphs (up to $2^{48}$) obtained from Boolean networks -- a modelling framework commonly appearing in systems biology.

We introduce FRAT, a new proof format for unsatisfiable SAT problems, and its associated toolchain. Compared to DRAT, the FRAT format allows solvers to include more information in proofs to reduce the computational cost of subsequent elaboration to LRAT. The format is easy to parse forward and backward, and it is extensible to future proof methods. The provision of optional proof steps allows SAT solver developers to balance implementation effort against elaboration time, with little to no overhead on solver time. We benchmark our FRAT toolchain against a comparable DRAT toolchain and confirm >84% median reduction in elaboration time and >94% median decrease in peak memory usage.

Timed automata (TA) have been widely adopted as a suitable formalism to model time-critical systems. Furthermore, contemporary model-checking tools allow the designer to check whether a TA complies with a system specification. However, the exact timing constants are often uncertain during the design phase. Consequently, the designer is often able to build a TA with a correct structure, however, the timing constants need to be tuned to satisfy the specification. Moreover, even if the TA initially satisfies the specification, it can be the case that just a slight perturbation during the implementation causes a violation of the specification. Unfortunately, model-checking tools are usually not able to provide any reasonable guidance on how to fix the model in such situations. In this paper, we propose several concepts and techniques to cope with the above mentioned design phase issues when dealing with reachability and safety specifications.

We introduce a generalization of the bisimulation game that finds distinguishing Hennessy-Milner logic formulas from every finitary, subformula-closed language in van Glabbeek's linear-time--branching-time spectrum between two finite-state processes. We identify the relevant dimensions that measure expressive power to yield formulas belonging to the coarsest distinguishing behavioral preorders and equivalences; the compared processes are equivalent in each coarser behavioral equivalence from the spectrum. We prove that the induced algorithm can determine the best fit of (in)equivalences for a pair of processes.

We develop a framework for model checking infinite-state systems by automatically augmenting them with auxiliary variables, enabling quantifier-free induction proofs for systems that would otherwise require quantified invariants. We combine this mechanism with a counterexample-guided abstraction refinement scheme for the theory of arrays. Our framework can thus, in many cases, reduce inductive reasoning with quantifiers and arrays to quantifier-free and array-free reasoning. We evaluate the approach on a wide set of benchmarks from the literature. The results show that our implementation often outperforms state-of-the-art tools, demonstrating its practical potential.

The model of asynchronous programming arises in many contexts, from low-level systems software to high-level web programming. We take a language-theoretic perspective and show general decidability and undecidability results for asynchronous programs that capture all known results as well as show decidability of new and important classes. As a main consequence, we show decidability of safety, termination and boundedness verification for higher-order asynchronous programs -- such as OCaml programs using Lwt -- and undecidability of liveness verification already for order-2 asynchronous programs. We show that under mild assumptions, surprisingly, safety and termination verification of asynchronous programs with handlers from a language class are decidable iff emptiness is decidable for the underlying language class. Moreover, we show that configuration reachability and liveness (fair termination) verification are equivalent, and decidability of these problems implies decidability of the well-known "equal-letters" problem on languages. Our results close the decidability frontier for asynchronous programs.