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In formal logic, model checking designates the problem of determining whether a formula ϕ evaluates to true or false in an interpretation K, written K |= ϕ. This problem finds applications in computer science: for example, K might represent a knowledge base and ϕ could be a query of which we wish to determine if it is implied by the knowledge in the base. We are then interested in finding efficient algorithms for determining whether K |= ϕ holds. In this chapter, we are interested in applications where K represents a system and ϕ a formula that represents a correctness property of this system. Typically, the systems we are interested in are reactive, that is, they interact repeatedly with their environment. They are often more concerned with control than with data and are usually composed of several components operating in parallel. Starting from a simple lift control application, we present basic ideas and concepts of verification algorithms in this context. The first publications about model checking appeared in 1981 by Clarke and Emerson [CLA 81] and by Queille and Sifakis [QUE 81]. Since then much progress has been made, and model checking has left the academic domain to enter mainstream development, notably of embedded systems and of communication protocols. Advances in the theory and application of model checking are reported in several important international conferences (including CAV, CHARME, and TACAS).The inputs of the model checker are a description of the system to be analyzed and the property to verify. The tool either confirms that the property is true in the model or informs the user that it does not hold. In that case, the model checker will Chapter written by Stephan MERZ. 8182 Modeling and Verification of Real-Time Systems also provide a counter-example: a run of the system that violates the property. This answer helps find the reason for the failure and has significantly contributed to the success of model checking in practice. Unfortunately, in practice model checking does not always yield such clear-cut results because the resource requirements (in terms of execution time and memory needed) can prohibit verifying more than an approximate model of the system. The positive outcome of model checking then no longer guaranteed the correctness of the system and, reciprocally, an error found by the model checker may be due to an inaccurate abstraction of the system. Model checking is therefore not a substitute for standard procedures to ensure system quality, but it is an additional technique that can help discover design problems at early stages of system development.This chapter is intended as an introduction to the fundamental concepts and techniques of algorithmic verification. It reflects a necessarily subjective reading of the (abundant) studies. We try to give many references to original work so that the chapter can be read as an annotated bibliography. More extensive presentations of the subject can be found in books and more detailed articles, including [BÉR 01, CLA 99, CLA 00, HUT 04]. ...
In formal logic, model checking designates the problem of determining whether a formula ϕ evaluates to true or false in an interpretation K, written K |= ϕ. This problem finds applications in computer science: for example, K might represent a knowledge base and ϕ could be a query of which we wish to determine if it is implied by the knowledge in the base. We are then interested in finding efficient algorithms for determining whether K |= ϕ holds. In this chapter, we are interested in applications where K represents a system and ϕ a formula that represents a correctness property of this system. Typically, the systems we are interested in are reactive, that is, they interact repeatedly with their environment. They are often more concerned with control than with data and are usually composed of several components operating in parallel. Starting from a simple lift control application, we present basic ideas and concepts of verification algorithms in this context. The first publications about model checking appeared in 1981 by Clarke and Emerson [CLA 81] and by Queille and Sifakis [QUE 81]. Since then much progress has been made, and model checking has left the academic domain to enter mainstream development, notably of embedded systems and of communication protocols. Advances in the theory and application of model checking are reported in several important international conferences (including CAV, CHARME, and TACAS).The inputs of the model checker are a description of the system to be analyzed and the property to verify. The tool either confirms that the property is true in the model or informs the user that it does not hold. In that case, the model checker will Chapter written by Stephan MERZ. 8182 Modeling and Verification of Real-Time Systems also provide a counter-example: a run of the system that violates the property. This answer helps find the reason for the failure and has significantly contributed to the success of model checking in practice. Unfortunately, in practice model checking does not always yield such clear-cut results because the resource requirements (in terms of execution time and memory needed) can prohibit verifying more than an approximate model of the system. The positive outcome of model checking then no longer guaranteed the correctness of the system and, reciprocally, an error found by the model checker may be due to an inaccurate abstraction of the system. Model checking is therefore not a substitute for standard procedures to ensure system quality, but it is an additional technique that can help discover design problems at early stages of system development.This chapter is intended as an introduction to the fundamental concepts and techniques of algorithmic verification. It reflects a necessarily subjective reading of the (abundant) studies. We try to give many references to original work so that the chapter can be read as an annotated bibliography. More extensive presentations of the subject can be found in books and more detailed articles, including [BÉR 01, CLA 99, CLA 00, HUT 04]. ...
International audienceLinear Relation Analysis [CH78, Hal79] is one of the first, but still one of the most powerful, abstract interpretations working in an infinite lattice. As such, it makes use of a widening operator to enforce the convergence of fixpoint computations. While the approximation due to widening can be arbitrarily refined by delaying the application of widening, the analysis quickly becomes too expensive with the increase of delay. Previous attempts at improving the precision of widening are not completely satisfactory, since none of them is guaranteed to improve the precision of the result, and they can nevertheless increase the cost of the analysis. In this paper, we investigate an improvement of Linear Relation Analysis consisting in computing, when possible, the exact (abstract) effect of a loop. This technique is fully compatible with the use of widening, and whenever it applies, it improves both the precision and the performance of the analysis
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