Model checking for linear temporal logic: An efficient implementation

This report provides evidence to support the claim that model checking for linear temporal logic (LTL) is practically efficient. Two implementations of a linear temporal logic model checker is described. One is based on transforming the model checking problem into a satisfiability problem; the other checks an LTL formula for a finite model by computing the cross-product of the finite state transition graph of the program with a structure containing all possible models for the property. An experiment was done with a set of mutual exclusion algorithms and tested safety and liveness under fairness for these algorithms

Micrometric particles twodimensional self-assembly during drying of liquid film

We computed the self-organisation process of a monodisperse collection of spherical micrometric particles trapped in a two-dimensional (2D) thin liquid film isothermally dried on a chemically inert substrate. The substrate is either flat or indented to create linear stripes on its surface. The numerical results are illustrated and discussed in the light of experimental ones obtained from the drying of diamond particles water based suspension ($d_{50} = 10 \mu m$) on a glass substrate. The drying of the suspension on a flat substrate leads to the formation of linear patterns and small clusters of micrometric particles distributed over the whole surface of the substrate, whereas the drying of the suspension on a indented substrate leads to the aggregation of the particles along one side of the stripe which has a higher roughness than the other side of the stripe. This is an easy experimental way to obtain colloidal selforganized patterns.Comment: 16 pages 7 figure

Allen Linear (Interval) Temporal Logic --Translation to LTL and Monitor Synthesis--

The relationship between two well established formalisms for temporal reasoning is first investigated, namely between Allen's interval algebra (or Allen's temporal logic, abbreviated \ATL) and linear temporal logic (\LTL). A discrete variant of \ATL is defined, called Allen linear temporal logic (\ALTL), whose models are \omega-sequences of timepoints, like in \LTL. It is shown that any \ALTL formula can be linearly translated into an equivalent \LTL formula, thus enabling the use of \LTL techniques and tools when requirements are expressed in \ALTL. %This translation also implies the NP-completeness of \ATL satisfiability. Then the monitoring problem for \ALTL is discussed, showing that it is NP-complete despite the fact that the similar problem for \LTL is EXPSPACE-complete. An effective monitoring algorithm for \ALTL is given, which has been implemented and experimented with in the context of planning applications

Undersampled Phase Retrieval with Outliers

We propose a general framework for reconstructing transform-sparse images from undersampled (squared)-magnitude data corrupted with outliers. This framework is implemented using a multi-layered approach, combining multiple initializations (to address the nonconvexity of the phase retrieval problem), repeated minimization of a convex majorizer (surrogate for a nonconvex objective function), and iterative optimization using the alternating directions method of multipliers. Exploiting the generality of this framework, we investigate using a Laplace measurement noise model better adapted to outliers present in the data than the conventional Gaussian noise model. Using simulations, we explore the sensitivity of the method to both the regularization and penalty parameters. We include 1D Monte Carlo and 2D image reconstruction comparisons with alternative phase retrieval algorithms. The results suggest the proposed method, with the Laplace noise model, both increases the likelihood of correct support recovery and reduces the mean squared error from measurements containing outliers. We also describe exciting extensions made possible by the generality of the proposed framework, including regularization using analysis-form sparsity priors that are incompatible with many existing approaches.Comment: 11 pages, 9 figure

Abstract Interpretation of Stateful Networks

Modern networks achieve robustness and scalability by maintaining states on their nodes. These nodes are referred to as middleboxes and are essential for network functionality. However, the presence of middleboxes drastically complicates the task of network verification. Previous work showed that the problem is undecidable in general and EXPSPACE-complete when abstracting away the order of packet arrival. We describe a new algorithm for conservatively checking isolation properties of stateful networks. The asymptotic complexity of the algorithm is polynomial in the size of the network, albeit being exponential in the maximal number of queries of the local state that a middlebox can do, which is often small. Our algorithm is sound, i.e., it can never miss a violation of safety but may fail to verify some properties. The algorithm performs on-the fly abstract interpretation by (1) abstracting away the order of packet processing and the number of times each packet arrives, (2) abstracting away correlations between states of different middleboxes and channel contents, and (3) representing middlebox states by their effect on each packet separately, rather than taking into account the entire state space. We show that the abstractions do not lose precision when middleboxes may reset in any state. This is encouraging since many real middleboxes reset, e.g., after some session timeout is reached or due to hardware failure

Test generation from P systems using model checking

This paper presents some testing approaches based on model checking and using different testing criteria. First, test sets are built from different Kripke structure representations. Second, various rule coverage criteria for transitional, non-deterministic, cell-like P systems, are considered in order to generate adequate test sets. Rule based coverage criteria (simple rule coverage, context-dependent rule coverage and variants) are defined and, for each criterion, a set of LTL (Linear Temporal Logic) formulas is provided. A codification of a P system as a Kripke structure and the sets of LTL properties are used in test generation: for each criterion, test cases are obtained from the counterexamples of the associated LTL formulas, which are automatically generated from the Kripke structure codification of the P system. The method is illustrated with an implementation using a specific model checker, NuSMV. (C) 2010 Elsevier Inc. All rights reserved

Efficient Symmetry Reduction and the Use of State Symmetries for Symbolic Model Checking

One technique to reduce the state-space explosion problem in temporal logic model checking is symmetry reduction. The combination of symmetry reduction and symbolic model checking by using BDDs suffered a long time from the prohibitively large BDD for the orbit relation. Dynamic symmetry reduction calculates representatives of equivalence classes of states dynamically and thus avoids the construction of the orbit relation. In this paper, we present a new efficient model checking algorithm based on dynamic symmetry reduction. Our experiments show that the algorithm is very fast and allows the verification of larger systems. We additionally implemented the use of state symmetries for symbolic symmetry reduction. To our knowledge we are the first who investigated state symmetries in combination with BDD based symbolic model checking

Fair termination revisited - with delay

AbstractA proof method for establishing the fair termination and total correctness of both nondeterministic and concurrent programs is presented. The method calls for the extension of state by auxiliary delay variables which count down to the instant in which certain action will be scheduled. It then uses well-founded ranking to prove fair termination allowing nested fair selection and loops

The Small Model Property: How Small Can It Be?

AbstractEfficient decision procedures for equality logic (quantifier-free predicate calculus+the equality sign) are of major importance when proving logical equivalence between systems. We introduce an efficient decision procedure for the theory of equality based on finite instantiations. The main idea is to analyze the structure of the formula and compute accordingly a small domain to each variable such that the formula is satisfiable iff it can be satisfied over these domains. We show how the problem of finding these small domains can be reduced to an interesting graph theoretic problem. This method enabled us to verify formulas containing hundreds of integer and floating point variables that could not be efficiently handled with previously known techniques