Enriched MU-Calculi Module Checking

The model checking problem for open systems has been intensively studied in the literature, for both finite-state (module checking) and infinite-state (pushdown module checking) systems, with respect to Ctl and Ctl*. In this paper, we further investigate this problem with respect to the \mu-calculus enriched with nominals and graded modalities (hybrid graded Mu-calculus), in both the finite-state and infinite-state settings. Using an automata-theoretic approach, we show that hybrid graded \mu-calculus module checking is solvable in exponential time, while hybrid graded \mu-calculus pushdown module checking is solvable in double-exponential time. These results are also tight since they match the known lower bounds for Ctl. We also investigate the module checking problem with respect to the hybrid graded \mu-calculus enriched with inverse programs (Fully enriched \mu-calculus): by showing a reduction from the domino problem, we show its undecidability. We conclude with a short overview of the model checking problem for the Fully enriched Mu-calculus and the fragments obtained by dropping at least one of the additional constructs

The Complexity of Enriched Mu-Calculi

The fully enriched μ-calculus is the extension of the propositional μ-calculus with inverse programs, graded modalities, and nominals. While satisfiability in several expressive fragments of the fully enriched μ-calculus is known to be decidable and ExpTime-complete, it has recently been proved that the full calculus is undecidable. In this paper, we study the fragments of the fully enriched μ-calculus that are obtained by dropping at least one of the additional constructs. We show that, in all fragments obtained in this way, satisfiability is decidable and ExpTime-complete. Thus, we identify a family of decidable logics that are maximal (and incomparable) in expressive power. Our results are obtained by introducing two new automata models, showing that their emptiness problems are ExpTime-complete, and then reducing satisfiability in the relevant logics to these problems. The automata models we introduce are two-way graded alternating parity automata over infinite trees (2GAPTs) and fully enriched automata (FEAs) over infinite forests. The former are a common generalization of two incomparable automata models from the literature. The latter extend alternating automata in a similar way as the fully enriched μ-calculus extends the standard μ-calculus.Comment: A preliminary version of this paper appears in the Proceedings of the 33rd International Colloquium on Automata, Languages and Programming (ICALP), 2006. This paper has been selected for a special issue in LMC

Low-Latency Millimeter-Wave Communications: Traffic Dispersion or Network Densification?

This paper investigates two strategies to reduce the communication delay in future wireless networks: traffic dispersion and network densification. A hybrid scheme that combines these two strategies is also considered. The probabilistic delay and effective capacity are used to evaluate performance. For probabilistic delay, the violation probability of delay, i.e., the probability that the delay exceeds a given tolerance level, is characterized in terms of upper bounds, which are derived by applying stochastic network calculus theory. In addition, to characterize the maximum affordable arrival traffic for mmWave systems, the effective capacity, i.e., the service capability with a given quality-of-service (QoS) requirement, is studied. The derived bounds on the probabilistic delay and effective capacity are validated through simulations. These numerical results show that, for a given average system gain, traffic dispersion, network densification, and the hybrid scheme exhibit different potentials to reduce the end-to-end communication delay. For instance, traffic dispersion outperforms network densification, given high average system gain and arrival rate, while it could be the worst option, otherwise. Furthermore, it is revealed that, increasing the number of independent paths and/or relay density is always beneficial, while the performance gain is related to the arrival rate and average system gain, jointly. Therefore, a proper transmission scheme should be selected to optimize the delay performance, according to the given conditions on arrival traffic and system service capability

Model Checking the Quantitative mu-Calculus on Linear Hybrid Systems

We study the model-checking problem for a quantitative extension of the modal mu-calculus on a class of hybrid systems. Qualitative model checking has been proved decidable and implemented for several classes of systems, but this is not the case for quantitative questions that arise naturally in this context. Recently, quantitative formalisms that subsume classical temporal logics and allow the measurement of interesting quantitative phenomena were introduced. We show how a powerful quantitative logic, the quantitative mu-calculus, can be model checked with arbitrary precision on initialised linear hybrid systems. To this end, we develop new techniques for the discretisation of continuous state spaces based on a special class of strategies in model-checking games and present a reduction to a class of counter parity games.Comment: LMCS submissio

A Uniform Substitution Calculus for Differential Dynamic Logic

This paper introduces a new proof calculus for differential dynamic logic (dL) that is entirely based on uniform substitution, a proof rule that substitutes a formula for a predicate symbol everywhere. Uniform substitutions make it possible to rely on axioms rather than axiom schemata, substantially simplifying implementations. Instead of nontrivial schema variables and soundness-critical side conditions on the occurrence patterns of variables, the resulting calculus adopts only a finite number of ordinary dL formulas as axioms. The static semantics of differential dynamic logic is captured exclusively in uniform substitutions and bound variable renamings as opposed to being spread in delicate ways across the prover implementation. In addition to sound uniform substitutions, this paper introduces differential forms for differential dynamic logic that make it possible to internalize differential invariants, differential substitutions, and derivations as first-class axioms in dL

Abstract Interpretation for Probabilistic Termination of Biological Systems

In a previous paper the authors applied the Abstract Interpretation approach for approximating the probabilistic semantics of biological systems, modeled specifically using the Chemical Ground Form calculus. The methodology is based on the idea of representing a set of experiments, which differ only for the initial concentrations, by abstracting the multiplicity of reagents present in a solution, using intervals. In this paper, we refine the approach in order to address probabilistic termination properties. More in details, we introduce a refinement of the abstract LTS semantics and we abstract the probabilistic semantics using a variant of Interval Markov Chains. The abstract probabilistic model safely approximates a set of concrete experiments and reports conservative lower and upper bounds for probabilistic termination