Satisfiability Modulo Theories (SMT) problem is a decision problem for logical first order formulas with respect to combinations of background theories such as: arithmetic, bit-vectors, arrays, and uninterpreted functions. Z3 is a new and efficient SMT Solver freely available from Microsoft Research. It is used in various software verification and analysis applications.

https://link.springer.com/content/pdf/10.1007%2F978-3-540-78800-3_24.pdf

Z3: an efficient SMT solver

Lots of learning tasks require dealing with graph data which contains rich relation information among elements. Modeling physics systems, learning molecular fingerprints, predicting protein interface, and classifying diseases demand a model to learn from graph inputs. In other domains such as learning from non-structural data like texts and images, reasoning on extracted structures (like the dependency trees of sentences and the scene graphs of images) is an important research topic which also needs graph reasoning models. Graph neural networks (GNNs) are neural models that capture the dependence of graphs via message passing between the nodes of graphs. In recent years, variants of GNNs such as graph convolutional network (GCN), graph attention network (GAT), graph recurrent network (GRN) have demonstrated ground-breaking performances on many deep learning tasks. In this survey, we propose a general design pipeline for GNN models and discuss the variants of each component, systematically categorize the applications, and propose four open problems for future research.

Graph Neural Networks: A Review of Methods and Applications

Artificial intelligence (AI) has undergone a renaissance recently, making major progress in key domains such as vision, language, control, and decision-making. This has been due, in part, to cheap data and cheap compute resources, which have fit the natural strengths of deep learning. However, many defining characteristics of human intelligence, which developed under much different pressures, remain out of reach for current approaches. In particular, generalizing beyond one's experiences--a hallmark of human intelligence from infancy--remains a formidable challenge for modern AI. 
The following is part position paper, part review, and part unification. We argue that combinatorial generalization must be a top priority for AI to achieve human-like abilities, and that structured representations and computations are key to realizing this objective. Just as biology uses nature and nurture cooperatively, we reject the false choice between "hand-engineering" and "end-to-end" learning, and instead advocate for an approach which benefits from their complementary strengths. We explore how using relational inductive biases within deep learning architectures can facilitate learning about entities, relations, and rules for composing them. We present a new building block for the AI toolkit with a strong relational inductive bias--the graph network--which generalizes and extends various approaches for neural networks that operate on graphs, and provides a straightforward interface for manipulating structured knowledge and producing structured behaviors. We discuss how graph networks can support relational reasoning and combinatorial generalization, laying the foundation for more sophisticated, interpretable, and flexible patterns of reasoning. As a companion to this paper, we have released an open-source software library for building graph networks, with demonstrations of how to use them in practice.

Relational inductive biases, deep learning, and graph networks

A code clone is a code portion in source files that is identical or similar to another. Since code clones are believed to reduce the maintainability of software, several code clone detection techniques and tools have been proposed. This paper proposes a new clone detection technique, which consists of the transformation of input source text and a token-by-token comparison. For its implementation with several useful optimization techniques, we have developed a tool, named CCFinder (Code Clone Finder), which extracts code clones in C, C++, Java, COBOL and other source files. In addition, metrics for the code clones have been developed. In order to evaluate the usefulness of CCFinder and metrics, we conducted several case studies where we applied the new tool to the source code of JDK, FreeBSD, NetBSD, Linux, and many other systems. As a result, CCFinder has effectively found clones and the metrics have been able to effectively identify the characteristics of the systems. In addition, we have compared the proposed technique with other clone detection techniques.

/pdf/ccfinder-a-multilinguistic-token-based-code-clone-detection-3uimzrhga0.pdf

CCFinder: a multilinguistic token-based code clone detection system for large scale source code

ing WS1S Systems to Verify Parameterized Networks . . . . . . . . . . . . 188 Kai Baukus, Saddek Bensalem, Yassine Lakhnech and Karsten Stahl FMona: A Tool for Expressing Validation Techniques over Infinite State Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 J.-P. Bodeveix and M. Filali Transitive Closures of Regular Relations for Verifying Infinite-State Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 Bengt Jonsson and Marcus Nilsson Diagnostic and Test Generation Using Static Analysis to Improve Automatic Test Generation . . . . . . . . . . . . . 235 Marius Bozga, Jean-Claude Fernandez and Lucian Ghirvu Efficient Diagnostic Generation for Boolean Equation Systems . . . . . . . . . . . . 251 Radu Mateescu Efficient Model-Checking Compositional State Space Generation with Partial Order Reductions for Asynchronous Communicating Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 Jean-Pierre Krimm and Laurent Mounier Checking for CFFD-Preorder with Tester Processes . . . . . . . . . . . . . . . . . . . . . . . 283 Juhana Helovuo and Antti Valmari Fair Bisimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Thomas A. Henzinger and Sriram K. Rajamani Integrating Low Level Symmetries into Reachability Analysis . . . . . . . . . . . . . 315 Karsten Schmidt Model-Checking Tools Model Checking Support for the ASM High-Level Language . . . . . . . . . . . . . . 331 Giuseppe Del Castillo and Kirsten Winter Table of

Tools and Algorithms for the Construction and Analysis of Systems. Proc. TACAS 2009

Z3 [3] is a state-of-the-art Satisfiability Modulo Theories (SMT) solver freely available from Microsoft Research. It solves the decision problem for quantifier-free formulas with respect to combinations of theories, such as arithmetic, bit-vectors, arrays, and uninterpreted functions. Z3 is used in various software analysis and test-case generation projects at Microsoft Research and elsewhere. The requirements from the user-base range from establishing validity, dually unsatisfiability, of firstorder formulas; to identify invalid, dually satisfiable, formulas. In both cases, there is often a need for more than just a yes/no answer from the prover. A model can exhibit why an invalid formula is not provable, and a proof-object can certify the validity of a formula. This paper describes the proof-producing internals of Z3. We also briefly introduce the model-producing facilities. We emphasize two features that can be of general interest: (1) we introduce a notion of implicit quotation to avoid introducing auxiliary variables, it simplifies the creation of proof objects considerably; (2) we produce natural deduction style proofs to facilitate modular proof re-construction.

/pdf/proofs-and-refutations-and-z3-191y33mges.pdf

Proofs and Refutations, and Z3.

We describe a new algorithm for solving linear integer programming problems. The algorithm performs a DPLL style search for a feasible assignment, while using a novel cut procedure to guide the search away from the conflicting states.

/pdf/cutting-to-the-chase-solving-linear-integer-arithmetic-3mum90quyx.pdf

Cutting to the Chase solving linear integer arithmetic

We present a new Simplex-based linear arithmetic solver that can be integrated efficiently in the DPLL(T ) framework. The new solver improves over existing approaches by enabling fast backtracking, supporting a priori simplification to reduce the problem size, and providing an efficient form of theory propagation. We also present a new and simple approach for solving strict inequalities. Experimental results show substantial performance improvements over existing tools that use other Simplex-based solvers in DPLL( T ) decision procedures. The new solver is even competitive with state-of-the-art tools specialized for the difference logic fragment.

/pdf/integrating-simplex-with-dpll-t-49815n7x8a.pdf

Integrating Simplex with DPLL(T )

In the past decade, Satisfiability Modulo Theories (SMT) solvers have been used successfully in a variety of applications including verification, automated theorem proving, and synthesis. While such solvers are highly adept at handling ground constraints in several decidable background theories, they primarily rely on heuristic quantifier instantiation methods such as E-matching to process quantified formulas. The success of these methods is often hindered by an overproduction of instantiations which makes ground level reasoning difficult. We introduce a new technique that alleviates this shortcoming by first discovering instantiations that are in conflict with the current state of the solver. The solver only resorts to traditional heuristic methods when such instantiations cannot be found, thus decreasing its dependence upon E-matching. Our experimental results show that our technique significantly reduces the number of instantiations required by an SMT solver to answer "unsatisfiable" for several benchmark libraries, and consequently leads to improvements over state-of-the-art implementations.

http://lara.epfl.ch/~reynolds/pres-quantify14.pdf

Finding Conflicting Instances of Quantified Formulas in SMT

The annual Satisfiability Modulo Theories Competition (SMT-COMP) was initiated in 2005 in order to stimulate the advance of state-of-the-art techniques and tools developed by the Satisfiability Modulo Theories (SMT) community. This paper summarizes the first six editions of the competition. We present the evolution of the competition's organization and rules, show how the state of the art has improved over the course of the competition, and discuss the impact SMT-COMP has had on the SMT community and beyond. Additionally, we include an exhaustive list of all competitors, and present experimental results showing significant improvement in SMT solvers during these six years. Finally, we analyze to what extent the initial goals of the competition have been achieved, and sketch future directions for the competition.

https://tpbin.com/uploads/subjects/7e82a97f-3e4e-484b-ac45-85ba114d1a5c.pdf

Leonardo de Moura

Papers

Proofs and Refutations, and Z3.

Cutting to the Chase solving linear integer arithmetic

Integrating Simplex with DPLL(T )

Finding Conflicting Instances of Quantified Formulas in SMT

6 Years of SMT-COMP