scholarly journals Computing Small Unsatisfiable Cores in Satisfiability Modulo Theories

2011 ◽  
Vol 40 ◽  
pp. 701-728 ◽  
Author(s):  
A. Cimatti ◽  
A. Griggio ◽  
R. Sebastiani
Keyword(s):  
Empirical Test ◽  
Main Idea ◽  
Satisfiability Modulo Theories ◽  
Smt Solver ◽  
The Core ◽  
Reduction Techniques ◽  
Novel Approach ◽  
Suitable Amount ◽  
Core Reduction ◽  
Unsatisfiable Core

The problem of finding small unsatisfiable cores for SAT formulas has recently received a lot of interest, mostly for its applications in formal verification. However, propositional logic is often not expressive enough for representing many interesting verification problems, which can be more naturally addressed in the framework of Satisfiability Modulo Theories, SMT. Surprisingly, the problem of finding unsatisfiable cores in SMT has received very little attention in the literature. In this paper we present a novel approach to this problem, called the Lemma-Lifting approach. The main idea is to combine an SMT solver with an external propositional core extractor. The SMT solver produces the theory lemmas found during the search, dynamically lifting the suitable amount of theory information to the Boolean level. The core extractor is then called on the Boolean abstraction of the original SMT problem and of the theory lemmas. This results in an unsatisfiable core for the original SMT problem, once the remaining theory lemmas are removed. The approach is conceptually interesting, and has several advantages in practice. In fact, it is extremely simple to implement and to update, and it can be interfaced with every propositional core extractor in a plug-and-play manner, so as to benefit for free of all unsat-core reduction techniques which have been or will be made available. We have evaluated our algorithm with a very extensive empirical test on SMT-LIB benchmarks, which confirms the validity and potential of this approach.

scholarly journals Syntax-Guided Quantifier Instantiation

2021 ◽  
pp. 145-163
Author(s):  
Aina Niemetz ◽  
Mathias Preiner ◽  
Andrew Reynolds ◽  
Clark Barrett ◽  
Cesare Tinelli
Keyword(s):  
State Of The Art ◽  
Satisfiability Modulo Theories ◽  
Floating Point ◽  
New Approach ◽  
Smt Solver ◽  
Floating Point Arithmetic ◽  
Novel Approach ◽  
Non Linear ◽  
Quantifier Instantiation ◽  
Point Arithmetic

AbstractThis paper presents a novel approach for quantifier instantiation in Satisfiability Modulo Theories (SMT) that leverages syntax-guided synthesis (SyGuS) to choose instantiation terms. It targets quantified constraints over background theories such as (non)linear integer, reals and floating-point arithmetic, bit-vectors, and their combinations. Unlike previous approaches for quantifier instantiation in these domains which rely on theory-specific strategies, the new approach can be applied to any (combined) theory, when provided with a grammar for instantiation terms for all sorts in the theory. We implement syntax-guided instantiation in the SMT solver CVC4, leveraging its support for enumerative SyGuS. Our experiments demonstrate the versatility of the approach, showing that it is competitive with or exceeds the performance of state-of-the-art solvers on a range of background theories.

Leveraging Control Flow Knowledge in SMT Solving of Program Verification

2021 ◽  
Vol 30 (4) ◽  
pp. 1-26
Author(s):  
Jianhui Chen ◽  
Fei He
Keyword(s):  
Program Verification ◽  
Search Space ◽  
General Purpose ◽  
Control Flow ◽  
Satisfiability Modulo Theories ◽  
Useful Knowledge ◽  
Smt Solver ◽  
Software Analysis ◽  
Smt Solving ◽  
Novel Approach

Satisfiability modulo theories (SMT) solvers have been widely applied as the reasoning engine for diverse software analysis and verification technologies. The efficiency of the SMT solver has significant effects on the performance of these technologies. However, current SMT solvers are designed for the general purpose of constraint solving. Lots of useful knowledge of programs cannot be utilized during SMT solving. As a result, the SMT solver may spend much effort to explore redundant search space. In this article, we propose a novel approach to utilizing control-flow knowledge in SMT solving. With this technique, the search space can be considerably reduced, and the efficiency of SMT solving is observably improved. We conducted extensive experiments on credible benchmarks. The results show significant improvements of our approach.

Applications and Challenges in Satisfiability Modulo Theories

10.29007/cl74 ◽  
2018 ◽  
Author(s):  
Leonardo De Moura ◽  
Nikolaj Bjorner
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Satisfiability Modulo Theories ◽  
Smt Solver ◽  
Invariant Generation ◽  
Software Analysis ◽  
The Core ◽  
Precise Analysis ◽  
System States ◽  
Automatic Theorem

The area of software analysis, testing and verification is now undergoing a revolution thanks to the use of automated and scalable support for logical methods. A well-recognized premise is that at the core of software analysis engines is invariably a component using logical formulas for describing states and transformations between system states. One can thus say that symbolic logic is the calculus of computation. The process of using this information for discovering and checking program properties (including such important properties as safety and security) amounts to automatic theorem proving. In particular, theorem provers that directly support common software constructs offer a compelling basis. Such provers are commonly called satisfiability modulo theories (SMT) solvers.Z3 is the leading SMT solver. It is developed by the authors at Microsoft Research. It can be used to check the satisfiability of logical formulas over one or more theories such as arithmetic, bit-vectors, lists, records and arrays.This paper examines three applications of Z3 in the context of invariant generation.The first lets Z3 infer invariants as a constraint satisfaction problem, the second applicationillustrates the use of Z3 for bit-precise analysis and our third application exemplifiesusing Z3 for calculations.

Engineering Theories with Z3

10.29007/x7b4 ◽  
2018 ◽  
Author(s):  
Nikolaj Bjorner
Keyword(s):  
Satisfiability Modulo Theories ◽  
Smt Solver ◽  
Testing Tools ◽  
Software And Hardware ◽  
Design And Testing

Modern Satisfiability Modulo Theories (SMT)solvers are fundamental to many programanalysis, verification, design and testing tools. They are a goodfit for the domain of software and hardware engineering becausethey support many domains that are commonly used by the tools.The meaning of domains are captured by theories that can beaxiomatized or supported by efficient <i>theory solvers</i>.Nevertheless, not all domains are handled by all solvers andmany domains and theories will never be native to any solver.We here explore different theories that extend MicrosoftResearch's SMT solver Z3's basicsupport. Some can be directly encoded or axiomatized,others make use of user theory plug-ins.Plug-ins are a powerful way for tools to supply their custom domains.

scholarly journals Principles of adaptive element spacing in linear array antennas

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tanzeela Mitha ◽  
Maria Pour
Keyword(s):  
Antenna Arrays ◽  
Communication Systems ◽  
Linear Array ◽  
Main Idea ◽  
Phase Center ◽  
Array Configuration ◽  
Array Antennas ◽  
Center Location ◽  
Novel Approach ◽  
Array Performance

AbstractA novel approach to linear array antennas with adaptive inter-element spacing is presented for the first time. The main idea is based upon electronically displacing the phase center location of the antenna elements, which determine their relative coordinates in the array configuration. This is realized by employing dual-mode microstrip patch antennas as a constitutive element, whose phase center location can be displaced from its physical center by simultaneously exciting two modes. The direction and the amount of displacement is controlled by the amplitude and phase of the modes at the element level. This in turn facilitates reconfiguring the inter-element spacing at the array level. For instance, a uniformly-spaced array could be electronically transformed into a non-uniform one without any mechanical means. The proposed idea is demonstrated in two- and three-element linear antenna arrays. The technique has the potential to control the radiation characteristics such as sidelobe levels, position of the nulls, and the beamwidths in small arrays, which are useful for adaptively controlling the array performance in emerging wireless communication systems and radars.

scholarly journals Can inner and outer containment counteract pulls and pushes toward delinquency? A test of Walter Reckless’s containment theory

2021 ◽  
pp. 147737082098881
Author(s):  
Heleen J Janssen ◽  
Gerben JN Bruinsma ◽  
Frank M Weerman
Keyword(s):  
Empirical Test ◽  
Linear Regression Analysis ◽  
Longitudinal Survey ◽  
External Factors ◽  
Interaction Theory ◽  
Theoretical Concepts ◽  
The Core ◽  
Longitudinal Survey Data ◽  
The Hague ◽  
The City

The aim of the current study is to provide an empirical test of containment theory of Walter Reckless (1899–1988). The theory proposes that outer and inner containment hold adolescents back from delinquency even when external factors pull and push them toward it. This early control theory was ahead of its time, but never received the empirical attention it deserves. This article outlines the core theoretical concepts and the basic propositions in order to empirically examine their validity. We employed hybrid linear regression analysis using longitudinal survey data of 612 adolescents (12–18 years old) in the city of The Hague, the Netherlands. The results indicate that outer and inner containment can be meaningfully distinguished, and that several but not all propositions of the theory are supported. Inner and outer containment function as a buffer against external pulls and are able to counteract the effect of increases in environmental pulls during adolescence. We conclude that containment theory is still a promising interaction theory that can help us understand why adolescents who experience external pulls toward delinquency are able to resist these influences.

scholarly journals SMT-Based Contention-Free Task Mapping and Scheduling on 2D/3D SMART NoC with Mixed Dimension-Order Routing

2022 ◽  
Vol 19 (1) ◽  
pp. 1-21
Author(s):  
Daeyeal Lee ◽  
Bill Lin ◽  
Chung-Kuan Cheng
Keyword(s):  
System Performance ◽  
Search Space ◽  
Satisfiability Modulo Theories ◽  
Low Latency ◽  
Task Mapping ◽  
Single Cycle ◽  
Space Reduction ◽  
Reduction Techniques ◽  
2D And 3D ◽  
Mixed Dimension

SMART NoCs achieve ultra-low latency by enabling single-cycle multiple-hop transmission via bypass channels. However, contention along bypass channels can seriously degrade the performance of SMART NoCs by breaking the bypass paths. Therefore, contention-free task mapping and scheduling are essential for optimal system performance. In this article, we propose an SMT (Satisfiability Modulo Theories)-based framework to find optimal contention-free task mappings with minimum application schedule lengths on 2D/3D SMART NoCs with mixed dimension-order routing. On top of SMT’s fast reasoning capability for conditional constraints, we develop efficient search-space reduction techniques to achieve practical scalability. Experiments demonstrate that our SMT framework achieves 10× higher scalability than ILP (Integer Linear Programming) with 931.1× (ranges from 2.2× to 1532.1×) and 1237.1× (ranges from 4× to 4373.8×) faster average runtimes for finding optimum solutions on 2D and 3D SMART NoCs and our 2D and 3D extensions of the SMT framework with mixed dimension-order routing also maintain the improved scalability with the extended and diversified routing paths, resulting in reduced application schedule lengths throughout various application benchmarks.

scholarly journals A Novel Approach for Robust Perceptual Image Hashing

2021 ◽  
Vol 14 (3) ◽  
pp. 38
Author(s):  
Azhar Hadmi ◽  
Awatif Rouijel
Keyword(s):  
Side Information ◽  
Main Idea ◽  
Jpeg Compression ◽  
Image Hashing ◽  
Novel Approach ◽  
Perceptual Hash ◽  
Short Signature ◽  
Robust Image ◽  
Tampered Image ◽  
The Stability

Perceptual image hashing system generates a short signature called perceptual hash attached to an image before transmission and acts as side information for analyzing the trustworthiness of the received image. In this paper, we propose a novel approach to improve robustness for perceptual image hashing scheme for generating a perceptual hash that should be resistant to content-preserving manipulations, such as JPEG compression and Additive white Gaussian noise (AWGN) also should differentiate the maliciously tampered image and its original version. Our algorithm first constructs a robust image, derived from the original input by analyzing the stability of the extracted features and improving their robustness. From the robust image, which does perceptually resemble the original input, we further extract the final robust features. Next, robust features are suitably quantized allowing the generation of the final perceptual hash using the cryptographic hash function SHA1. The main idea of this paper is to transform the original image into a more robust one that allows the extraction of robust features. Generation of the robust image turns out be quite important since it introduces further robustness to the perceptual image hashing system. The paper can be seen as an attempt to propose a general methodology for more robust perceptual image hashing. The experimental results presented in this paper reveal that the proposed scheme offers good robustness against JPEG compression and Additive white Gaussian noise.

scholarly journals Integration Development of Urban Agglomeration in Central Liaoning, China, by Trajectory Gravity Model

2021 ◽  
Vol 10 (10) ◽  
pp. 698
Author(s):  
Ruren Li ◽  
Shoujia Li ◽  
Zhiwei Xie
Keyword(s):  
Gravity Model ◽  
Gravitational Force ◽  
Main Idea ◽  
Correlation Coefficients ◽  
Urban Agglomeration ◽  
Economic Research ◽  
The Core ◽  
Proposed Model ◽  
Two Indices ◽  
Spatial Trajectory

Integration development of urban agglomeration is important for regional economic research and management. In this paper, a method was proposed to study the integration development of urban agglomeration by trajectory gravity model. It can analyze the gravitational strength of the core city to other cities and characterize the spatial trajectory of its gravitational direction, expansion, etc. quantitatively. The main idea is to do the fitting analysis between the urban axes and the gravitational lines. The correlation coefficients retrieved from the fitting analysis can reflect the correlation of two indices. For the different cities in the same year, a higher value means a stronger relationship. There is a clear gravitational force between the cities when the value above 0.75. For the most cities in different years, the gravitational force between the core city with itself is increasing by years. At the same time, the direction of growth of the urban axes tends to increase in the direction of the gravitational force between cities. There is a clear tendency for the trajectories of the cities to move closer together. The proposed model was applied to the integration development of China Liaoning central urban agglomeration from 2008 to 2016. The results show that cities are constantly attracted to each other through urban gravity.

Explaining Algorithms

2011 ◽  
pp. 2261-2279
Author(s):  
Tomasz Muldner ◽  
Elhadi Shakshuki
Keyword(s):  
Distance Education ◽  
Main Idea ◽  
Top Down ◽  
Levels Of Abstraction ◽  
Visualization System ◽  
Client Server ◽  
Novel Approach ◽  
Visualization Systems ◽  
Explanation System ◽  
Server Architecture

This article presents a novel approach for explaining algorithms that aims to overcome various pedagogical limitations of the current visualization systems. The main idea is that at any given time, a learner is able to focus on a single problem. This problem can be explained, studied, understood, and tested, before the learner moves on to study another problem. Toward this end, a visualization system that explains algorithms at various levels of abstraction has been designed and implemented. In this system, each abstraction is focused on a single operation from the algorithm using various media, including text and an associated visualization. The explanations are designed to help the user to understand basic properties of the operation represented by this abstraction, for example its invariants. The explanation system allows the user to traverse the hierarchy graph, using either a top-down (from primitive operations to general operations) approach or a bottom-up approach. Since the system is implemented using a client-server architecture, it can be used both in the classroom setting and through distance education.

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