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10:30 | Regular Model Checking Upside-Down: An Invariant-Based Approach ABSTRACT. Regular model checking is a well-established technique for the verification of infinite-state systems whose configurations can be represented as finite words over a suitable alphabet. It applies to systems whose set of initial configurations is regular, and whose transition relation is captured by a length-preserving transducer. To verify safety properties, regular model checking iteratively computes automata recognizing increasingly larger regular sets of reachable configurations, and checks if they contain unsafe configurations. Since this procedure often does not terminate, acceleration, abstraction, and widening techniques have been developed to compute a regular superset of the set of reachable configurations. In this paper we develop a complementary approach. Instead of approaching the set of reachable configurations from below, we start with the set of all configurations and compute increasingly smaller regular supersets of it. We use that the set of reachable configurations is equal to the intersection of all inductive invariants of the system. Since the intersection is in general non-regular, we introduce $b$-bounded invariants, defined as those representable by CNF-formulas with at most $b$ clauses. We prove that, for every $b \geq 0$, the intersection of all $b$-bounded inductive invariants is regular, and show how to construct an automaton recognizing it. Finally, we study the complexity of deciding if this automaton accepts some unsafe configuration. We show that the problem is in \textsc{EXPSPACE} for every $b \geq 0$, and \textsc{PSPACE}-complete for $b=1$. Finally, we study the performance of our approach in a number of benchmarks. |

11:00 | On an Invariance Problem for Parameterized Concurrent Systems PRESENTER: Lucas Bueri ABSTRACT. We consider concurrent systems consisting of replicated finite-state processes that synchronize via joint interactions in a network with user-defined topology. The system is specified using a resource logic with a multiplicative connective and inductively defined predicates, reminiscent of Separation Logic. The problem we consider is if a given formula in this logic defines an invariant, namely whether any model of the formula, following an arbitrary firing sequence of interactions, is transformed into another model of the same formula. This property, called \emph{havoc invariance}, is quintessential in proving the correctness of reconfiguration programs that change the structure of the network at runtime. We show that the havoc invariance problem is many-one reducible to the entailment problem $\phi \models \psi$, asking if any model of $\phi$ is also a model of $\psi$. Although, in general, havoc invariance is found to be undecidable, this reduction allows to prove that havoc invariance is in 2EXP, for a general fragment of the logic, with a 2EXP entailment problem. |

11:30 | Towards Concurrent Quantitative Separation Logic PRESENTER: Ira Fesefeldt ABSTRACT. In this paper, we develop a novel verification technique to reason about programs featuring concurrency, pointers and randomization. While the integration of concurrency and pointers is well studied, little is known about the combination of all three paradigms. To close this gap, we combine two kinds of separation logic - Quantitative Separation Logic and Concurrent Separation Logic - into a new separation logic able to reason about lower bounds of the probability to realize a postcondition after executing such a program. |

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