Dense Integer-Complete Synthesis for Bounded Parametric Timed Automata

Ensuring the correctness of critical real-time systems, involving concurrent behaviors and timing requirements, is crucial. Timed automata extend finite-state automata with clocks, compared in guards and invariants with integer constants. Parametric timed automata (PTAs) extend timed automata with timing parameters. Parameter synthesis aims at computing dense sets of valuations for the timing parameters, guaranteeing a good behavior. However, in most cases, the emptiness problem for reachability (i.e., whether the emptiness of the parameter valuations set for which some location is reachable) is undecidable for PTAs and, as a consequence, synthesis procedures do not terminate in general, even for bounded parameters. In this paper, we introduce a parametric extrapolation, that allows us to derive an underapproximation in the form of linear constraints containing not only all the integer points ensuring reachability, but also all the (non-necessarily integer) convex combinations of these integer points, for general PTAs with a bounded parameter domain. We also propose two further algorithms synthesizing parameter valuations guaranteeing unavoidability, and preservation of the untimed behavior w.r.t. a reference parameter valuation, respectively. Our algorithms terminate and can output constraints arbitrarily close to the complete result. We demonstrate their applicability and efficiency using the tool Rom\'eo on two classical benchmarks.Comment: This is an extended version of the paper by the same authors published in the proceedings of the 9th International Workshop on Reachability Problems (RP 2015

Coverability Synthesis in Parametric Petri Nets

We study Parametric Petri Nets (PPNs), i.e., Petri nets for which some arc weights can be parameters. In that setting, we address a problem of parameter synthesis, which consists in computing the exact set of values for the parameters such that a given marking is coverable in the instantiated net. Since the emptiness of that solution set is already undecidable for general PPNs, we address a special case where parameters are used only as input weights (preT-PPNs), and consequently for which the solution set is downward-closed. To this end, we invoke a result for the representation of upward closed set from Valk and Jantzen. To use this procedure, we show we need to decide universal coverability, that is decide if some marking is coverable for every possible values of the parameters. We therefore provide a proof of its EXPSPACE-completeness, thus settling the previously open problem of its decidability. We also propose an adaptation of this reasoning to the case of parameters used only as output weights (postT-PPNs). In this case, the condition to use this procedure can be reduced to the decidability of the existential coverability, that is decide if there exists values of the parameters making a given marking coverable. This problem is known decidable but we provide here a cleaner proof, providing its EXPSPACE-completeness, by reduction to Omega Petri Nets

Reachability and liveness in parametric timed automata

We study timed systems in which some timing features are unknown parameters. Parametric timed automata (PTAs) are a classical formalism for such systems but for which most interesting problems are undecidable. Notably, the parametric reachability emptiness problem, i.e., whether at least one parameter valuation allows to reach some given discrete state, is undecidable. Lower-bound/upper-bound parametric timed automata (L/U-PTAs) achieve decidability for reachability properties by enforcing a separation of parameters used as upper bounds in the automaton constraints, and those used as lower bounds. In this paper, we first study reachability. We exhibit a subclass of PTAs (namely integer-points PTAs) with bounded rational-valued parameters for which the parametric reachability emptiness problem is decidable. Using this class, we present further results improving the boundary between decidability and undecidability for PTAs and their subclasses such as L/U-PTAs. We then study liveness. We prove that: (1) the existence of at least one parameter valuation for which there exists an infinite run in an L/U-PTA is PSPACE-complete; (2) the existence of a parameter valuation such that the system has a deadlock is however undecidable; (3) the problem of the existence of a valuation for which a run remains in a given set of locations exhibits a very thin border between decidability and undecidability.Comment: This manuscript is an extended version of two conference papers published in the proceedings of ICFEM 2016 and ACSD 201

Reachability and liveness in parametric timed automata

We study timed systems in which some timing features are unknown parameters. Parametric timed automata (PTAs) are a classical formalism for such systems but for which most interesting problems are undecidable. Notably, the parametric reachability emptiness problem, i.e., the emptiness of the parameter valuations set allowing to reach some given discrete state, is undecidable. Lower-bound/upper-bound parametric timed automata (L/U-PTAs) achieve decidability for reachability properties by enforcing a separation of parameters used as upper bounds in the automaton constraints, and those used as lower bounds. In this paper, we first study reachability. We exhibit a subclass of PTAs (namely integer-points PTAs) with bounded rational-valued parameters for which the parametric reachability emptiness problem is decidable. Using this class, we present further results improving the boundary between decidability and undecidability for PTAs and their subclasses such as L/U-PTAs. We then study liveness. We prove that: (1) deciding the existence of at least one parameter valuation for which there exists an infinite run in an L/U-PTA is PSpace-complete; (2) the existence of a parameter valuation such that the system has a deadlock is however undecidable; (3) the problem of the existence of a valuation for which a run remains in a given set of locations exhibits a very thin border between decidability and undecidability

Pomsets and Unfolding of Reset Petri Nets

International audienceReset Petri nets are a particular class of Petri nets where transition firings can remove all tokens from a place without checking if this place actually holds tokens or not. In this paper we look at partial order semantics of such nets. In particular, we propose a pomset bisimulation for comparing their concurrent behaviours. Building on this pomset bisimulation we then propose a generalization of the standard finite complete prefixes of unfolding to the class of safe reset Petri nets

A temporary social parasite of tropical plant-ants improves the fitness of a myrmecophyte

Myrmecophytes offer plant-ants a nesting place in exchange for protection from their enemies, particularly defoliators. These obligate ant-plant mutualisms are common model systems for studying factors that allow horizontally transmitted mutualisms to persist since parasites of ant-myrmecophyte mutualisms exploit the rewards provided by host plants whilst providing no protection in return. In pioneer formations in French Guiana, Azteca alfari and Azteca ovaticeps are known to be mutualists of myrmecophytic Cecropia (Cecropia ants). Here, we show that Azteca andreae, whose colonies build carton nests on myrmecophytic Cecropia, is not a parasite of Azteca-Cecropia mutualisms nor is it a temporary social parasite of A. alfari; it is, however, a temporary social parasite of A. ovaticeps. Contrarily to the two mutualistic Azteca species that are only occasional predators feeding mostly on hemipteran honeydew and food bodies provided by the host trees, A. andreae workers, which also attend hemipterans, do not exploit the food bodies. Rather, they employ an effective hunting technique where the leaf margins are fringed with ambushing workers, waiting for insects to alight. As a result, the host trees' fitness is not affected as A. andreae colonies protect their foliage better than do mutualistic Azteca species resulting in greater fruit production. Yet, contrarily to mutualistic Azteca, when host tree development does not keep pace with colony growth, A. andreae workers forage on surrounding plants; the colonies can even move to a non-Cecropia tree

Taxonomic assignment of uncultivated prokaryotic virus genomes is enabled by gene-sharing networks

© 2019, The Author(s), under exclusive licence to Springer Nature America, Inc. Microbiomes from every environment contain a myriad of uncultivated archaeal and bacterial viruses, but studying these viruses is hampered by the lack of a universal, scalable taxonomic framework. We present vConTACT v.2.0, a network-based application utilizing whole genome gene-sharing profiles for virus taxonomy that integrates distance-based hierarchical clustering and confidence scores for all taxonomic predictions. We report near-identical (96%) replication of existing genus-level viral taxonomy assignments from the International Committee on Taxonomy of Viruses for National Center for Biotechnology Information virus RefSeq. Application of vConTACT v.2.0 to 1,364 previously unclassified viruses deposited in virus RefSeq as reference genomes produced automatic, high-confidence genus assignments for 820 of the 1,364. We applied vConTACT v.2.0 to analyze 15,280 Global Ocean Virome genome fragments and were able to provide taxonomic assignments for 31% of these data, which shows that our algorithm is scalable to very large metagenomic datasets. Our taxonomy tool can be automated and applied to metagenomes from any environment for virus classification

Hybrid modeling of biological networks: mixing temporal and qualitative biological properties

<p>Abstract</p> <p>Background</p> <p>Modeling a dynamical biological system is often a difficult task since the a <it>priori </it>unknown parameters of such models are not always directly given by the experiments. Despite the lack of experimental quantitative knowledge, one can see a dynamical biological system as (i) the combined evolution tendencies (increase or decrease) of the biological compound concentrations, and: (ii) the temporal features, such as delays between two concentration peaks (i.e. the times when one of the components completes an increase (resp. decrease) phase and starts a decrease (resp. increase) phase).</p> <p>Results</p> <p>We propose herein a new hybrid modeling framework that follows such biological assumptions. This hybrid approach deals with both a qualitative structure of the system and a quantitative structure. From a theoretical viewpoint, temporal specifications are expressed as equality or inequality constraints between delay parameters, while the qualitative specifications are expressed as an ordered pattern of the concentrations peaks of the components. Using this new hybrid framework, the temporal specifications of a biological system can be obtained from incomplete experimental data. The model may be processed by a hybrid model-checker (e.g. Phaver) which is able to give some new constraints on the delay parameters (e.g. the delay for a given transition is exactly 5 hours after the later peak of a gene product concentration). Furthermore, by using a constraint solver on the previous results, it becomes possible to get the set of parameters settings which are consistent with given specifications. Such a modeling approach is particularly accurate for modeling oscillatory biological behaviors like those observed in the Drosophila circadian cycles. The achieved results concerning the parameters of this oscillatory system formally confirm the several previous studies made by numerical simulations. Moreover, our analysis makes it possible to propose an automatic investigation of the respective impact of per and tim on the circadian cycle.</p> <p>Conclusions</p> <p>A new hybrid technique for an automatic formal analysis of biological systems is developed with a special emphasis on their oscillatory behaviors. It allows the use of incomplete and empirical biological data.</p