scholarly journals LTL with Arithmetic and its Applications in Reasoning about Hierarchical Systems

10.29007/wpg3 ◽  
2018 ◽  
Author(s):  
Rachel Faran ◽  
Orna Kupferman
Keyword(s):  
Model Checking ◽  
Blow Up ◽  
Satisfiability Problem ◽  
Theoretic Approach ◽  
Hierarchical Systems ◽  
Infinite Domain ◽  
Composite Systems ◽  
System A ◽  
Computational Bottleneck ◽  
Naive Model

The computational bottleneck in model-checking applications is the blow-up involved in the translation of systems to their mathematical model. This blow up is especially painful in systems with variables over an infinite domain, and in composite systems described by means of their underlying components. We introduce and study linear temporal logic with arithmetic (LTLA, for short), where formulas include variables that take values in Z, and in which linear arithmetic over these values is supported. We develop an automata-theoretic approach for reasoning about LTLA formulas and use it in order to solve, in PSPACE, the satisfiability problem for the existential fragment of LTLA and the model-checking problem for its universal fragment. We show that these results are tight, as a single universally- quantified variable makes the satisfiability problem for LTLA undecidable.In addition to reasoning about systems with variables over Z, we suggest applications of LTLA in reasoning about hierarchical systems, which consist of subsystems that can call each other in a hierarchical manner. We use the values in Z in order to describe the nesting depth of components in the system. A naive model-checking algorithm for hierarchical systems flattens them, which involves an exponential blow up. We suggest a model-checking algorithm that avoids the flattening and avoids a blow up in the number of components.

scholarly journals Improved model checking of hierarchical systems

2012 ◽  
Vol 210 ◽  
pp. 68-86 ◽  
Author(s):  
Benjamin Aminof ◽  
Orna Kupferman ◽  
Aniello Murano
Keyword(s):  
Model Checking ◽  
Hierarchical Systems ◽  
Improved Model

scholarly journals Properties of composite systems based on polymethylsiloxane and silica in the water environment

Surface ◽  
2020 ◽  
Vol 12(27) ◽  
pp. 100-136
Author(s):  
T. V. Krupska ◽  
◽  
V. M. Gun'ko ◽  
I. S. Protsak ◽  
I. I. Gerashchenko ◽  
...  
Keyword(s):  
Interfacial Energy ◽  
Composite System ◽  
Close Contact ◽  
Water Environment ◽  
Heterogeneous Systems ◽  
Adsorption Properties ◽  
Mechanical Loads ◽  
Composite Systems ◽  
System A ◽  
Hydrophilic Particles

The formation of a composite system based on equal amounts of hydrophobic, porous polymethylsiloxane and hydrophilic nanosilicon A-300 was studied. It is shown that during the formation of a composite system the specific surface of the material is significantly reduced, which is due to the close contact between hydrophobic and hydrophilic particles. When water is added to the composite system, in the process of homogenization under conditions of dosed mechanical loading, the effect of nanocoagulation is manifested – the formation of nanosized particles of hydrated silica inside the polymethylsiloxane matrix, recorded on TEM microphotographs. When measuring the value of the interfacial energy of PMS and PMS/A-300 composite by low-temperature 1H NMR spectroscopy, it was found that the effect of nanocoagulation is manifested in a decrease (compared to the original PMS) energy of water interaction with the surface of the composite obtained under small mechanical conditions. its growth when using high mechanical loads. In the process, the binding of water in heterogeneous systems containing PMS, pyrogenic nanosilica (A-300), water and surfactants – decamethoxine (DMT) was studied. Composite systems were created using metered mechanical loads. It is shown that when filling the interparticle gaps of PMS by the method of hydrosealing, the interphase energy of water in the interparticle gaps of hydrophobic PMS with the same hydration is twice the interfacial energy of water in hydrophilic silica A-300. This is due to the smaller linear dimensions of the interparticle gaps in PMS compared to A-300. In the composite system, A-300/PMS/DMT/H2O there are non-additive growth of binding energy of water, which is probably due to the formation, under the influence of mechanical stress in the presence of water, microheterogeneous areas consisting mainly of hydrophobic and hydrophilic components (microcoagulation). Thus, with the help of mechanical loads, you can control the adsorption properties of composite systems and create new materials with unique adsorption properties.

scholarly journals Modeling, Analysis, and Comparison of Nanotechnology System: A Graph-Theoretic Approach

2020 ◽  
Author(s):  
Tanvir Singh ◽  
V.P. Agrawal
Keyword(s):  
Graph Theory ◽  
Complete Analysis ◽  
Theoretic Model ◽  
Theoretic Approach ◽  
Graph Theoretic ◽  
Systems Model ◽  
System A ◽  
Modeling Analysis ◽  
Graph Theoretic Approach ◽  
Permanent Function

Nanotechnology can create many new nanomaterials and nanodevices with a vast range of applications, such as in medicine, electronics, biomaterials, and energy production, etc. An attempt is made to develop an integrated systems model for the structure of the nanotechnology system in terms of its constituents and interactions between the constituents and processes, etc. using graph theory and matrix algebra. The nanotechnology system is first modeled with the help of graph theory, secondly by variable adjacency matrix and thirdly by multinomial (which is known as a permanent function). The permanent function provides an opportunity to carry out a structural analysis of nanotechnology system in terms of its strength, weakness, improvement, and optimization, by correlating the different systems with its structure. The physical meaning has been associated with each term of the permanent function. Different structural attributes of the nanotechnology system are identified concurrently to reduce cost, time for design and development, and also to develop a graph-theoretic model, matrix model, and multinomial permanent model of nanotechnology system. The top-down approach for a complete analysis of any nanotechnology systems is given. The general methodology is presented for the characterization and comparison of two nanotechnology systems.

scholarly journals From Timed Automata to Logic - and Back

1995 ◽  
Vol 2 (2) ◽  
Author(s):  
Francois Laroussinie ◽  
Kim G. Larsen ◽  
Carsten Weise
Keyword(s):  
Model Checking ◽  
Real Time ◽  
Timed Automata ◽  
Finite Automata ◽  
Automatic Verification ◽  
Satisfiability Problem ◽  
Timed Automaton

One of the most successful techniques for automatic verification is that<br />of model checking. For finite automata there exist since long extremely<br />efficient model-checking algorithms, and in the last few years these algorithms have been made applicable to the verification of real-time automata using the region-techniques of Alur and Dill.<br />In this paper, we continue this transfer of existing techniques from the<br />setting of finite (untimed) automata to that of timed automata. In particular, a timed logic L is put forward, which is sufficiently expressive that we for any timed automaton may construct a single characteristic L formula uniquely characterizing the automaton up to timed bisimilarity. Also, we prove decidability of the satisfiability problem for L with respect to given bounds on the number of clocks and constants of the timed automata to be constructed. None of these results have as yet been succesfully accounted for in the presence of time.

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