Model checking has proven to be a successful technology to verify requirements and design for a variety of real-time embedded and safety-critical systems. Here's how it works. Before you even start writing code on a project, you face the chronic problem of software development: flawed design requirements. It makes sense to find flaws up front because flawed requirements breed bugs that you have to get rid of later, often at a high cost to the project and the bottom line. In the last decade or so, the computer science research community has made tremendous progress in developing tools and techniques for verifying requirements and design.
Listing Extreeme An SMV model description and requirements list. Li, D. Please join the Simons Foundation and our generous member organizations in supporting arXiv during our giving campaign September October 21, Embedded Staff. The system should not attempt to switch the pump off on if it's already off on. Stotts, M. In fact, there may be parts of your requirements that may be difficult or even impossible to model in the given modeling notation. Figure Mmodel Initial part of the execution tree for the pump controller system View a full-sized version of this image. Mauborgne, A.
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Henzinger, R. Rosu, editors. Emerson  by J. This general concept applies chdcking many Exreme of logic and suitable structures. Nelson, J. Verification: Theory and Practice pp Cite as. To this end, the problem is formulated as a task in logicnamely to check whether a given structure satisfies a given logical formula. Java Report4 5 —38, The Extreme model checking Extreme is a residential Extreme model checking combining the functions of a routernetwork switchwireless access point and NAS as well as varied other functions, and one of Apple's former AirPort products. Princeton University Press, Hatcliff, C.
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- Verification: Theory and Practice pp Cite as.
- The AirPort Extreme is a residential gateway combining the functions of a router , network switch , wireless access point and NAS as well as varied other functions, and one of Apple's former AirPort products.
- To Zohar, for teaching me about logic and life.
- Apple periodically offers software updates called firmware updates that improve AirPort performance, security, and functionality.
- In computer science , model checking , or property checking , is, for a given finite-state model of a system, exhaustively and automatically checking whether this model meets a given specification a.
Model checking has proven to be a successful technology to verify requirements and design for a variety of real-time embedded and safety-critical systems. Here's how it works. Before you even start writing code on a project, you face the chronic problem of software development: flawed design requirements.
It makes sense to find flaws up front because flawed requirements breed bugs that you have to get rid of later, often at a high cost to the project and the bottom line.
In the last decade or so, the computer science research community has made tremendous progress in developing tools and techniques for verifying requirements and design. The most successful approach that's emerged is called model checking.
When combined with strict use of a formal modeling language, you can automate your verification process fairly well. In this article, I'll introduce you to model checking and show you how it works. Colossal task It's common to write design requirements heavily in English, interlaced with suitable tables, diagrams, screen shots, and UML descriptions, such as use cases and diagrams for instance, sequence, class, and state transition diagrams.
When we check design requirements, we're basically seeking the answers to a series of questions. Here are the general questions you'll ask when checking your requirements:. Finding the answers to these questions is a tall order and there's no easy way to do it, but if your requirements can jump successfully through these hoops, you've got a good foundation for a sound system. Despite some help from modeling tools such as UML, the problem of ensuring the quality of requirements remains.
The process is heavily manual and time consuming, involving reviews and sometimes partial prototyping. Using multiple notations such as those in UML introduces additional problems:.
The cost of errors in requirements are often high, requiring at least rework and maintenance. If you implement the incorrect requirements as they are, it may lead to incorrect system behavior in the field and high costs, such as loss of life and property, particularly in real-time, embedded safety-critical systems. Similar problems exist in ensuring the quality of system design. One way to improve the quality of your requirements and design is to use automated tools to check the quality of various aspects of the requirements and design.
But what tools? Building tools to check requirements or design written in English is clearly extremely difficult. It's necessary to enforce a clear, rigorous, and unambiguous formal language for stating the requirements. If the language for writing requirements and design has well-defined semantics, it may be feasible to develop tools to analyze the statements written in that language.
This basic idea using a rigorous language for writing requirements or design is now acknowledged as a foundation for system verification. Figure 1: The model checking approach. Model checking Model checking is the most successful approach that's emerged for verifying requirements. The essential idea behind model checking is shown in Figure 1. A model-checking tool accepts system requirements or design called models and a property called specification that the final system is expected to satisfy.
The tool then outputs yes if the given model satisfies given specifications and generates a counterexample otherwise.
The counterexample details why the model doesn't satisfy the specification. By studying the counterexample, you can pinpoint the source of the error in the model, correct the model, and try again.
The idea is that by ensuring that the model satisfies enough system properties, we increase our confidence in the correctness of the model. The system requirements are called models because they represent requirements or design. So what formal language works for defining models? There's no single answer, since requirements or design for systems in different application domains vary greatly.
For instance, requirements of a banking system and an aerospace system differ in size, structure, complexity, nature of system data, and operations performed.
Such control-oriented systems occur in a wide variety of domains: aerospace, avionics, automotive, biomedical instrumentation, industrial automation and process control, railways, nuclear power plants, and so forth. Even communication and security protocols in digital hardware systems can be thought of as control oriented. For control-oriented systems, finite state machines FSM are widely accepted as a good, clean, and abstract notation for defining requirements and design.
We also need to:. In short, we need extended finite state machines EFSM. Most model checking tools have their own rigorous formal language for defining models, but most of them are some variant of the EFSM.
A simple system model Let's look at how you can use model checking to verify properties of a simple embedded system. Of course, you can also write this model in most other model-checking tools. See the sidebar near the end of this article for a list of model-checking tools and where to find them. Figure 2: A simple two tank pumping system. Consider a simple pumping control system that transfers water from a source tank A into another sink tank B using a pump P, as shown in Figure 2.
Each tank has two level-meters: one to detect whether its level is empty and the other to detect whether its level is full.
The tank level is ok if it's neither empty nor full; in other words, if it's above the empty mark but below the full mark. Initially, both tanks are empty. The pump is to be switched on as soon as the water level in tank A reaches ok from empty , provided that tank B is not full. The pump remains on as long as tank A is not empty and as long as tank B is not full.
The pump is to be switched off as soon as either tank A becomes empty or tank B becomes full. The system should not attempt to switch the pump off on if it's already off on. While this example may appear trivial, it easily extends to a controller for a complex network of pumps and pipes to control multiple source and sink tanks, such as those in water treatment facilities or chemical production plants.
Listing 1 An SMV model description and requirements list. The model of this system in SMV is as follows and is shown in Listing 1. The first VAR section declares that the system has three state variables. Variable pump records whether the pump is on or off. A system state is defined by a tuple of values for each of these three variables. The INIT section, near the end, defines initial values for the variables here, initially the pump is assumed to be off but the other two variables can have any value.
Each next statement defines how the value of a particular variable changes. All these assignment statements are assumed to work in parallel; the next state is defined as the net result of executing all the assignment statements in this section. The lower tank can go from empty to the empty or ok state; from ok to either empty or full or remain ok if the pump is on; from ok to either ok or full if the pump is off; from full can't change state if the pump is off; from full to ok or full if the pump is on.
Similar changes are defined for the upper tank. Internally, most model-checking tools flatten or unfold an input model into a transition system called Kripke structure.
Unfolding involves removing hierarchies in the EFSM, removing parallel compositions, and removing guards and actions on transitions. Each state in the Kripke structure is essentially a tuple containing one value for each state variable.
A transition in Kripke structure denotes change in the value of one or more state variables. A given property is actually checked against the Kripke structure obtained by unfolding the given model. However, for the purposes of understanding what a property statement means, a Kripke structure is further unfolded into an infinite tree where each path in the tree indicates a possible execution or behavior of the system. Paths and specs Initially, the system could be in any of the nine states where there are no restrictions on the water level in A or B but the pump is assumed to be off.
Let's denote a state by an ordered tuple where A and B denote the current water level in tank A and B, and P denotes the current pump status. To illustrate, let's assume the initial state to be.
Then as per the system model, the next state from this state could be any of the ,. From the next state could be either of , , , , , or. For each of these states, we could calculate the next possible states. Figure 3: Initial part of the execution tree for the pump controller system View a full-sized version of this image. The states can be arranged in the form of an infinite execution or computation tree , where the root is labeled with our chosen initial state and the children of any state denote the next possible states as shown in Figure 3.
A system execution is a path in this execution tree. In general, the system has infinitely many such execution paths. The aim of model checking is to examine whether or not the execution tree satisfies a user-given property specification. The question now is how do we specify properties of paths and states in the paths of an execution tree? CTL is an extension of the usual Boolean propositional logic which includes the logical connectives such as and, or, not, implies where additional temporal connectives are available.
Table 1: Some temporal connectives in CTL. Figure 4: Intuition for CTL formulae which are satisfied at state s 0 View a full-sized version of this image. Table 1 and Figure 4 illustrate the intuitive meaning of some of the basic temporal connectives in CTL. Basically, E for some path and A for all paths are path quantifiers for paths beginning from a state.
F for some state and G for all states are state quantifiers for states in a path. Given a property and a possibly infinite computation tree T corresponding to the system model, a model-checking algorithm essentially examines T to check if T satisfies the property.
For example, consider a property AF g where g is a propositional formula not involving any CTL connectives. Figure 4b shows an example of a computation tree T.
If g is true at s 0 then we're done, since s 0 occurs in every path starting at s 0. But suppose g is not true in s 0. Then since every path from s 0 goes either to the left child or to the right child of s 0 , the property is true at s 0 if it's recursively checked to be true at both children of s 0 in T.
Figure 4b shows that g is true at the root of the left subtree indicated by the filled circle. Hence all paths from s 0 to left child and further down in the left subtree satisfy the property. Now suppose g is not true at the right child of s 0 ; hence the property is recursively checked for all its children. Figure 4b shows that g is true at all children of the right child of s 0 indicated by filled circles and hence the property is true for the right subtree of s 0.
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Verification: Theory and Practice pp Cite as. One of the central axioms of extreme programming is the disciplined use of regression testing during stepwise software development. Due to recent progress in software model checking, it has become possible to supplement this process with automatic checks for behavioral safety properties of programs, such as conformance with locking idioms and other programming protocols and patterns.
For efficiency reasons, all checks must be incremental, i. We show that the lazy-abstraction algorithm, and its implementation in Blast, can be extended to support the fully automatic and incremental checking of temporal safety properties during software development.
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