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Abstract. We consider parity games on infinite graphs where configurations are represented by control-states and integer vectors. This framework subsumes two classic game problems: parity games on vector addition systems with states (VASS) and multidimensional energy parity games. We show that the multidimensional energy parity game problem is inter-reducible with a subclass of singlesided parity games on VASS where just one player can modify the integer counters and the opponent can only change control-states. Our main result is that the minimal elements of the upward-closed winning set of these single-sided parity games on VASS are computable. This implies that the Pareto frontier of the minimal initial credit needed to win multidimensional energy parity games is also computable, solving an open question from the literature. Moreover, our main result implies the decidability of weak simulation preorder/equivalence between finite-state systems and VASS, and the decidability of model checking VASS with a large fragment of the modal µ-calculus.

We study decision problems for parameterized verification of protocols for ad hoc networks. The problem we consider is control state reachability for networks of arbitrary size. We restrict our analysis to topologies that approximate the notion of bounded diameter often used in ad hoc networks for optimizing broadcast communication. We show that restricting to graphs with bounded diameter is not sufficient to make control state reachability decidable, but the problem turns out to be decidable when considering an additionally restricted class of graphs that still includes cliques. Although decidable, the problem is already Ackermann-hard over clique graphs.

Abstract. We study the decidability status of model-checking freeze LTL over various subclasses of counter machines for which the reachability problem is known to be decidable (reversal-bounded counter machines, vector additions systems with states, flat counter machines, one-counter machines). In freeze LTL, a register can store a counter value and at some future position an equality test can be done between a register and a counter value. Herein, we complete an earlier work started on one-counter machines by considering other subclasses of counter machines, and especially the class of reversal-bounded counter machines. This gives us the opportuniy to provide a systematic classification that distinguishes determinism vs. nondeterminism and we consider subclasses of formulae by restricting the set of atomic formulae or/and the polarity of the occurrences of the freeze operators, leading to the flat fragment.

Abstract. We consider the model of Time Petri Nets where time is associated with transitions. Two semantics for time elapsing can be considered: the strong one, for which all transitions are urgent, and the weak one, for which time can elapse arbitrarily. It is well known that many verification problems such as the marking reachability are undecidable with the strong semantics. In this paper, we focus on Time Petri Nets with weak semantics equipped with three different memory policies for the firing of transitions. We prove that the reachability problem is decidable for the most common memory policy (intermediate) and becomes undecidable otherwise. Moreover, we study the relative expressiveness of these memory policies and obtain partial results.

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Abstract. We investigate the impact of node and communication failures on the decidability and complexity of parametric verification of a formal model of ad hoc networks. We start by considering three possible types of node failures: intermittence, restart, and crash. Then we move to three cases of communication failures: nondeterministic message loss, message loss due to conflicting emissions, and detectable conflicts. Interestingly, we prove that the considered decision problem (reachability of a control state) is decidable for node intermittence and message loss (either nondeterministic or due to conflicts) while it turns out to be undecidable for node restart/crash, and conflict detection.

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