Scope-bounded multistack pushdown systems: fixed-point, sequentialization, and tree-width

We present a novel fixed-point algorithm to solve reachability of multi-stack pushdown systems restricted to runs of bounded-scope. The followed approach is compositional, in the sense that the runs of the system are summarized by bounded-size interfaces. Moreover, it is suitable for a direct implementation and can be exploited to prove two new results. We give a sequentialization for this class of systems, i.e., for each such multi-stack pushdown system we construct an equivalent single-stack pushdown system that faithfully simulates the behaviour of each thread. We prove that the behaviour graphs (multiply nested words) for these systems have bounded three-width, and thus a number of decidability results can be derived from Courcelle’s theorem

On P-transitive graphs and applications

We introduce a new class of graphs which we call P-transitive graphs, lying between transitive and 3-transitive graphs. First we show that the analogue of de Jongh-Sambin Theorem is false for wellfounded P-transitive graphs; then we show that the mu-calculus fixpoint hierarchy is infinite for P-transitive graphs. Both results contrast with the case of transitive graphs. We give also an undecidability result for an enriched mu-calculus on P-transitive graphs. Finally, we consider a polynomial time reduction from the model checking problem on arbitrary graphs to the model checking problem on P-transitive graphs. All these results carry over to 3-transitive graphs.Comment: In Proceedings GandALF 2011, arXiv:1106.081

Visibly Pushdown Modular Games

Games on recursive game graphs can be used to reason about the control flow of sequential programs with recursion. In games over recursive game graphs, the most natural notion of strategy is the modular strategy, i.e., a strategy that is local to a module and is oblivious to previous module invocations, and thus does not depend on the context of invocation. In this work, we study for the first time modular strategies with respect to winning conditions that can be expressed by a pushdown automaton. We show that such games are undecidable in general, and become decidable for visibly pushdown automata specifications. Our solution relies on a reduction to modular games with finite-state automata winning conditions, which are known in the literature. We carefully characterize the computational complexity of the considered decision problem. In particular, we show that modular games with a universal Buchi or co Buchi visibly pushdown winning condition are EXPTIME-complete, and when the winning condition is given by a CARET or NWTL temporal logic formula the problem is 2EXPTIME-complete, and it remains 2EXPTIME-hard even for simple fragments of these logics. As a further contribution, we present a different solution for modular games with finite-state automata winning condition that runs faster than known solutions for large specifications and many exits.Comment: In Proceedings GandALF 2014, arXiv:1408.556

Type Inference for Bimorphic Recursion

This paper proposes bimorphic recursion, which is restricted polymorphic recursion such that every recursive call in the body of a function definition has the same type. Bimorphic recursion allows us to assign two different types to a recursively defined function: one is for its recursive calls and the other is for its calls outside its definition. Bimorphic recursion in this paper can be nested. This paper shows bimorphic recursion has principal types and decidable type inference. Hence bimorphic recursion gives us flexible typing for recursion with decidable type inference. This paper also shows that its typability becomes undecidable because of nesting of recursions when one removes the instantiation property from the bimorphic recursion.Comment: In Proceedings GandALF 2011, arXiv:1106.081

Buckling in FDM 3D printed PLA elements: a DIC-assisted experimental investigation

In the recent years, a lot of works has been done to understand if, and in what extent, Fused Deposition Modelling (FDM) could be shifted from prototyping to manufacturing of small productions or individual components. Several authors investigated the tensile mechanical properties of FDM 3D-printed elements under specific printing parameters. Other ones identified the influence of some of those parameters on tensile mechanical properties. Less attention was paid to compressive ones. In this work, the authors studied how short-length Polylactic Acid (PLA) 3D printed specimens behaved under compression. Due to the anisotropy of 3D FDM printed components, the out of plane direction was investigated in 3D printing reference system. In this context, the authors specifically focused on buckling phenomenon. A wide range of low slenderness ratio was considered, inside which the relation between the critical stress and the slenderness ratio was studied. An extensive experimental campaign was conducted: 10 different slenderness ratios were considered, and 10 specimens per each ratio were printed, tested and analyzed. The square prism geometry was used in this study. This choice limited the number of directions in which the buckling deflection could have happened. As a further advantage, it allowed the use of a single camera Digital Image Correlation system for buckling observation. Through this technique, the authors monitored the maps of the transverse displacement throughout the compression tests. In shortest specimens the transverse displacement map appeared to be symmetric with respect to the longitudinal axis throughout the test, with a single or a double barreling compression mode. In longer specimens the transverse displacement map kept symmetric up to the maximum load; a lateral deflection appeared right after. Analyzing the transverse displacement vs. compressive load curves, the authors determined the compressive critical loads. No significant differences arose among the critical loads in the considered slenderness ratio range. The authors evaluated the capability of classical analytical models for buckling critical load estimation in isotropic materials to predict FDM 3D printed PLA failures. The Linear Euler model, the Tangent Modulus theory and the Johnson’s formula were considered. The compressive mechanical properties and the tensile ones were determined before resorting to the listed models. FDM 3D printed PLA proved to have an asymmetric behavior in tensile-compressive properties: stiffer in traction, more resistant in compression. When the tensile mechanical properties were used in the above described models, the estimation of critical loads was unsatisfactory. On the contrary, the Tangent Modulus theory gave satisfactory but conservative estimations when the compressive mechanical properties were used in it

A 3D shell model for the thermal and hygroscopic stress analysis of composite and sandwich structures

A general 3D exact shell solution for the thermo-hygro-elastic analysis of a heterogeneous group of multi-layered composite and sandwich structures is proposed. The 3D equilibrium equations are written in orthogonal mixed curvilinear coordinates, they are valid for spherical shells and they automatically degenerate in those for simpler geometries. The elastic part of the proposed model is based on a layer-wise exact solution where the exponential matrix method allows to solve the differential equations through the thickness direction. Simply-supported boundary conditions and harmonic forms for each variable are employed. The temperature and moisture content amplitudes are imposed at the external surfaces in steady-state conditions. Therefore, the related profiles can be evaluated through the thickness direction in three different ways: - calculation of temperature and moisture content profiles using 3D Fourier heat conduction and 3D Fick diffusion equations, respectively; - evaluation of temperature and moisture content profiles using 1D version of Fourier heat conduction and Fick diffusion equations, respectively; - a priori assumed linear temperature and moisture content profiles through the thickness direction. After the definition of the temperature and moisture content profiles, they can be considered as known terms in the 3D differential equilibrium equations. A set of non-homogeneous second order differential equilibrium equations are obtained. After a reduction to a first order differential equation system, the exponential matrix method is used for both the general and the particular solutions. The effects of the temperature and moisture content fields on the static response of plates and shells are investigated for different thickness ratios, geometries, lamination schemes, materials and temperature/moisture content values. Results will demonstrate the importance in the 3D shell model of both the correct definition of the elastic part and the appropriate evaluation of the temperature and moisture content profiles through the thickness of the structures

Comparisons between strain gauges and digital image correlation in experimental testing of 3D printed PLA elements

The widespread Fused Filament Fabrication (FFF) is an additive manufacturing technique based on polymers. Recently, lots of researchers studied how 3D printed parts behave under load to design functional components. Whether for characterization or validation, mechanical tests are the primary tools; proper measuring displacements or strains is essential. The contact transducers, such as Strain Gauges (SG) for deformations or Linear Variable Differential (Inductive) Transformers (LVD(I)T) for displacements, are established instruments. However, when the tests involve materials with a low modulus of elasticity, the interaction between the sensor and the specimen might alter their output. Non-contact transducers, such as the Digital Image Correlation (DIC), do not suffer from these effects. In this work, the authors experimentally and numerically compared SG and DIC in testing 3D printed PLA components. Two sets of tensile specimens formed the test bench of this work. During the tests, SGs monitored the first set; SGs and DIC monitored the second one. The authors quantified the effect using the apparent moduli of elasticity and detected a local reinforcing effect. Specimens with bonded strain gauges appeared stiffer in terms of strains derived from the SGs themselves. However, the same specimens appeared to be consistent with the non-instrumented ones in terms of DIC strains, which allowed a global reinforcing effect to be excluded. A 2D Finite Element (FE) model was used to simulate these effects: 2D shell elements discretized both the specimens and the strain gauge, bonded together in the hypothesis of perfect adhesion. The strain gauge internal microstructure, a metal grid into polymeric layers, was simplified as an isotropic constitutive model with equivalent elastic modulus and Poisson ratio. The authors proposed a digital procedure to evaluate the volume fraction of the metal grid based on a high-resolution image of the transducer; through it, they estimated both the above equivalent mechanical properties. The simulation agreed with the experimental results: it confirmed the local reinforcing effect and its magnitude. This effect was present, although the SGs were specifically designed for low-modulus material. The estimated and equivalent elastic modulus of the strain gauge had the same order of magnitude as the tested PLA; this feature advised that the stiffening effect could worsen in even less-stiff materials. Strain gauges can still be necessary tools, mainly when the surfaces to be analyzed are not in sight and DIC tools are ineffective. In these circumstances, the authors’ experimental and numerical methods allow the output correction when calibration curves are not available

Sequentializing Parameterized Programs

We exhibit assertion-preserving (reachability preserving) transformations from parameterized concurrent shared-memory programs, under a k-round scheduling of processes, to sequential programs. The salient feature of the sequential program is that it tracks the local variables of only one thread at any point, and uses only O(k) copies of shared variables (it does not use extra counters, not even one counter to keep track of the number of threads). Sequentialization is achieved using the concept of a linear interface that captures the effect an unbounded block of processes have on the shared state in a k-round schedule. Our transformation utilizes linear interfaces to sequentialize the program, and to ensure the sequential program explores only reachable states and preserves local invariants.Comment: In Proceedings FIT 2012, arXiv:1207.348