A Full First-Order Constraint Solver for Decomposable Theories

AbstractWe present in this paper a first-order axiomatization of an extended theoryTof finite or infinite trees, built on a signature containing an infinite set of function symbols and a relationfinite(t), which enables to distinguish between finite and infinite trees. We show thatThas at least one model and prove its completeness by giving not only a decision procedure, but a full first-order constraint solver that gives clear and explicit solutions for any first-order constraint satisfaction problem inT. The solver is given in the form of 16 rewriting rules that transform any first-order constraintinto an equivalent disjunction φ of simple formulas such that φ is either the formulatrueor the formulafalseor a formula having at least one free variable, being equivalent neither totruenor tofalseand where the solutions of the free variables are expressed in a clear and explicit way. The correctness of our rules implies the completeness ofT. We also describe an implementation of our algorithm in CHR (Constraint Handling Rules) and compare the performance with an implementation in C++ and that of a recent decision procedure for decomposable theories.

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Applications and extensions of Alloy: past, present and future

Mathematical Structures in Computer Science ◽

10.1017/s0960129512000291 ◽

2013 ◽

Vol 23 (4) ◽

pp. 915-933 ◽

Cited By ~ 9

Author(s):

EMINA TORLAK ◽

MANA TAGHDIRI ◽

GREG DENNIS ◽

JOSEPH P. NEAR

Keyword(s):

Automated Analysis ◽

Test Case Generation ◽

Test Case ◽

Recent Application ◽

Code Verification ◽

Constraint Solver ◽

First Order ◽

The Core ◽

Automated Simulation ◽

Relational Logic

Alloy is a declarative language for lightweight modelling and analysis of software. The core of the language is based on first-order relational logic, which offers an attractive balance between analysability and expressiveness. The logic is expressive enough to capture the intricacies of real systems, but is also simple enough to support fully automated analysis with the Alloy Analyzer. The Analyzer is built on a SAT-based constraint solver and provides automated simulation, checking and debugging of Alloy specifications. Because of its automated analysis and expressive logic, Alloy has been applied in a wide variety of domains. These applications have motivated a number of extensions both to the Alloy language and to its SAT-based analysis. This paper provides an overview of Alloy in the context of its three largest application domains, lightweight modelling, bounded code verification and test-case generation, and three recent application-driven extensions, an imperative extension to the language, a compiler to executable code and a proof-capable analyser based on SMT.

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Experimental analysis on mechanical properties of BF/PLA composites and its lightweight design on power battery box

Proceedings of the Institution of Mechanical Engineers Part D Journal of Automobile Engineering ◽

10.1177/09544070211065862 ◽

2021 ◽

pp. 095440702110658

Author(s):

Ying Zhao ◽

Siqi Zheng ◽

Minghan Yan ◽

Xuanming Liu ◽

Binlin Wang ◽

...

Keyword(s):

Mechanical Properties ◽

Working Conditions ◽

Lightweight Design ◽

Mechanical Shock ◽

First Order ◽

Automotive Components ◽

Power Battery ◽

Element Simulation ◽

Order Constraint ◽

Modal Vibration

In response to the concept of energy conservation and environmental protection, a novel composite battery box with BF/PLA composite is proposed. Firstly, the mechanical properties of BF/PLA composite are tested, and it is concluded that the property parameters of BF/PLA composite with 50% BF mass fraction is selected as the material property parameter of subsequent finite element simulation. Subsequently, the statics analysis and constraint modal analysis of the traditional metal battery box are carried out under the typical working conditions of rapid turning and braking under vertical bumping. Based on this, the upper and lower box materials of the battery box except the bracket are replaced by BF/PLA composite. The morphology optimization, topology optimization and free size optimization are carried out with the constraint that the first-order modal vibration frequency is no less than 30 Hz. Compared with the traditional metal battery box, the stiffness and strength of the optimized BF/PLA composite battery box are significantly enhanced. Moreover, the first-order constraint modal frequency increases by 15.5%, and the comprehensive weight reduction ratio reaches 40.88%. Finally, the optimized BF/PLA composite battery box is verified under random vibration, mechanical shock analysis, collision analysis, extrusion and falling ball analysis and drop analysis conditions. Meanwhile, compared with the traditional metal battery box under the same working conditions, the excellent reliability of the composite battery box is highlighted. The proposed BF/PLA composite battery box satisfies the requirements of stiffness and strength performances under various working conditions, which provides theoretical and data support for the application of composite materials in battery box and other automotive components.

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