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

Model Checking

The Internet has led to the creation of a digital society, where (almost) everything is connected and is accessible from anywhere. However, despite their widespread adoption, traditional IP networks are complex and very hard to manage. It is both difficult to configure the network according to predefined policies, and to reconfigure it to respond to faults, load, and changes. To make matters even more difficult, current networks are also vertically integrated: the control and data planes are bundled together. Software-defined networking (SDN) is an emerging paradigm that promises to change this state of affairs, by breaking vertical integration, separating the network's control logic from the underlying routers and switches, promoting (logical) centralization of network control, and introducing the ability to program the network. The separation of concerns, introduced between the definition of network policies, their implementation in switching hardware, and the forwarding of traffic, is key to the desired flexibility: by breaking the network control problem into tractable pieces, SDN makes it easier to create and introduce new abstractions in networking, simplifying network management and facilitating network evolution. In this paper, we present a comprehensive survey on SDN. We start by introducing the motivation for SDN, explain its main concepts and how it differs from traditional networking, its roots, and the standardization activities regarding this novel paradigm. Next, we present the key building blocks of an SDN infrastructure using a bottom-up, layered approach. We provide an in-depth analysis of the hardware infrastructure, southbound and northbound application programming interfaces (APIs), network virtualization layers, network operating systems (SDN controllers), network programming languages, and network applications. We also look at cross-layer problems such as debugging and troubleshooting. In an effort to anticipate the future evolution of this new paradigm, we discuss the main ongoing research efforts and challenges of SDN. In particular, we address the design of switches and control platforms—with a focus on aspects such as resiliency, scalability, performance, security, and dependability—as well as new opportunities for carrier transport networks and cloud providers. Last but not least, we analyze the position of SDN as a key enabler of a software-defined environment.

https://publications.uni.lu/bitstream/10993/20596/1/survey_on_SDN.pdf

Software-Defined Networking: A Comprehensive Survey

This ebook is the first authorized digital version of Kernighan and Ritchie's 1988 classic, The C Programming Language (2nd Ed.). One of the best-selling programming books published in the last fifty years, "K&R" has been called everything from the "bible" to "a landmark in computer science" and it has influenced generations of programmers. Available now for all leading ebook platforms, this concise and beautifully written text is a "must-have" reference for every serious programmers digital library.

As modestly described by the authors in the Preface to the First Edition, this "is not an introductory programming manual; it assumes some familiarity with basic programming concepts like variables, assignment statements, loops, and functions. Nonetheless, a novice programmer should be able to read along and pick up the language, although access to a more knowledgeable colleague will help."

The C programming language

Software-Defined Networking (SDN) is an emerging paradigm that promises to change this state of affairs, by breaking vertical integration, separating the network's control logic from the underlying routers and switches, promoting (logical) centralization of network control, and introducing the ability to program the network. The separation of concerns introduced between the definition of network policies, their implementation in switching hardware, and the forwarding of traffic, is key to the desired flexibility: by breaking the network control problem into tractable pieces, SDN makes it easier to create and introduce new abstractions in networking, simplifying network management and facilitating network evolution. In this paper we present a comprehensive survey on SDN. We start by introducing the motivation for SDN, explain its main concepts and how it differs from traditional networking, its roots, and the standardization activities regarding this novel paradigm. Next, we present the key building blocks of an SDN infrastructure using a bottom-up, layered approach. We provide an in-depth analysis of the hardware infrastructure, southbound and northbound APIs, network virtualization layers, network operating systems (SDN controllers), network programming languages, and network applications. We also look at cross-layer problems such as debugging and troubleshooting. In an effort to anticipate the future evolution of this new paradigm, we discuss the main ongoing research efforts and challenges of SDN. In particular, we address the design of switches and control platforms -- with a focus on aspects such as resiliency, scalability, performance, security and dependability -- as well as new opportunities for carrier transport networks and cloud providers. Last but not least, we analyze the position of SDN as a key enabler of a software-defined environment.

Checking the satisfiability of logical formulas, SMT solvers scale orders of magnitude beyond custom ad hoc solvers.

Satisfiability modulo theories: introduction and applications

The IC3 algorithm was recently introduced for proving properties of finite state reactive systems. It has been applied very successfully to hardware model checking. We provide a specification of the algorithm using an abstract transition system and highlight its dual operation: model search and conflict resolution. We then generalize it along two dimensions. Along one dimension we address nonlinear fixed-point operators (push-down systems) and evaluate the algorithm on Boolean programs. In the second dimension we leverage proofs and models and generalize the method to Boolean constraints involving theories.

Generalized property directed reachability

Satisfiability Modulo Theories (SMT) solvers have proven highly scalable, efficient and suitable for integrating theory reasoning. However, for numerous applications from program analysis and verification, the ground fragment is insufficient, as proof obligations often include quantifiers. A well known approach for quantifier reasoning uses a matching algorithm that works against an E-graph to instantiate quantified variables. This paper introduces algorithms that identify matches on E-graphs incrementally and efficiently. In particular, we introduce an index that works on E-graphs, called E-matching code treesthat combine features of substitution and code trees, used in saturation based theorem provers. E-matching code trees allow performing matching against several patterns simultaneously. The code trees are combined with an additional index, called the inverted path index, which filters E-graph terms that may potentially match patterns when the E-graph is updated. Experimental results show substantial performance improvements over existing state-of-the-art SMT solvers.

Efficient E-Matching for SMT Solvers

i¾?Z is a part of the SMT solver Z3. It allows users to pose and solve optimization problems modulo theories. Many SMT applications use models to provide satisfying assignments, and a growing number of these build on top of Z3 to get optimal assignments with respect to objective functions. i¾?Z provides a portfolio of approaches for solving linear optimization problems over SMT formulas, MaxSMT, and their combinations. Objective functions are combined as either Pareto fronts, lexicographically, or each objective is optimized independently. We describe usage scenarios of i¾?Z, outline the tool architecture that allows dispatching problems to special purpose solvers, and examine use cases.

/pdf/vz-an-optimizing-smt-solver-4qj3igup8y.pdf

Nikolaj Bjørner

Papers

Z3: an efficient SMT solver

Satisfiability modulo theories: introduction and applications

Generalized property directed reachability

Efficient E-Matching for SMT Solvers

vZ - An Optimizing SMT Solver