## Verification of Real-Time Systems using Linear Relation Analysis (1997)

Venue: | FORMAL METHODS IN SYSTEM DESIGN |

Citations: | 117 - 6 self |

### BibTeX

@INPROCEEDINGS{Halbwachs97verificationof,

author = {Nicolas Halbwachs and Yann-Erick Proy and Patrick Roumanoff},

title = {Verification of Real-Time Systems using Linear Relation Analysis},

booktitle = {FORMAL METHODS IN SYSTEM DESIGN},

year = {1997},

pages = {157--185},

publisher = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

Linear Relation Analysis [CH78] is an abstract interpretation devoted to the automatic discovery of invariant linear inequalities among numerical variables of a program. In this paper, we apply such an analysis to the verification of quantitative time properties of two kinds of systems: synchronous programs and linear hybrid systems.

### Citations

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Citation Context ...ract semantic properties to be used in compilers, either for static consistency checks or for code optimization. Most of these techniques have been unified in the framework of abstract interpretation =-=[CC77]-=-. In this paper, we propose to adapt a specific abstract interpretation, called linear relation analysis, to the verification of real-time systems. Linear relation analysis [CH78] is a method to disco... |

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Citation Context ...Time Systems using Linear Relation Analysis Nicolas Halbwachs, Yann-Erick Proy, Patrick Roumanoff Verimag, Centre Equation 2, avenue de Vignate F-38610 Gieres,France Abstract Linear Relation Analysis =-=[CH78]-=- is an abstract interpretation devoted to the automatic discovery of invariant linear inequalities among numerical variables of a program. In this paper, we apply such an analysis to the verification ... |

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Citation Context ...ons. Each process has a critical section and at each instant, at most one of the two processes is allowed to be in its critical section. Mutual exclusion is ensured by a version of Fischer's protocol =-=[Lam87]-=-, which we describe first in pseudocode. The code executed by process P i (i = 1; 2) is shown beside. repeat repeat await k = 0 k := i delay b until k = i Critical section k := 0 forever The two proce... |

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Citation Context ...es also, the synchronous approach has some advantages: Since the parallel composition is synchronous, the desired properties of a program can be easily and modularly expressed by means of an observer =-=[HLR93]-=-, i.e., another program which observes the behavior of the first one and decides whether it is correct. The verification then consists in checking that the parallel composition of the program and its ... |

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Citation Context ... built on top of the library, allows the available operations to be interactively invoked. A prototype analyzer of hybrid automata. Automata are described in a hybrid extension of the Argos formalism =-=[Mar92]-=-. 3 For the same example, [HH94] solves the problem by changing the control structure of the automaton, by distinguishing the locations according to the values of k1 and k2 . They get exact results, b... |

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Citation Context ... extensions, to two classes of real-time systems: The first application concerns the verification of programs written in synchronous languages [IEE91, Hal93b], for properties involving delay counters =-=[Hal93a]-=-. Although these counters are bounded integer variables that could be taken into account by classical finite state methods, our analysis avoids the tremendous state explosion that would occur during s... |

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Citation Context ...). A minimal system of generator can be extracted from (V; R) by discarding all redundant vertices and rays, and keeping only one representative in each subset of mutually redundant vertices or rays. =-=[LeV92]-=- proposes an simpler and more efficient way to minimize a system of generators during its construction, based on the following remark: Let n 1 be the dimension of the least hyperplane containing P , a... |

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Citation Context ...ues are determined by the choice of the abstract domain, the design of a widening operator is based on heuristics. The following widening operator (hereafter called standard widening) was proposed in =-=[Hal79]-=-. Let P and Q be two polyhedra. Roughly speaking, the widening PrQ is obtained by removing from the system of P all the inequalities that are not satisfied by Q. Fig. 4.a shows an example where P = f(... |

32 |
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Citation Context ...states is prohibitive. So, the choice of a suitable control structure with respect to the property to be proved, is an important problem; the use of symbolic BDD-based techniques for the control part =-=[DWT95]-=- should be considered for that. A last solution, when the verification fails, is to apply backward analysis: Let Bad 0 be the set of states that violate the property and have been found reachable by t... |

31 |
Algorithm for discovering the set of all solutions of a linear programming problem
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Citation Context ...ere exist efficient algorithms [Che68, LeV92] for translating each representation into the other; these algorithms also minimize the representations. The principle of the translation is the following =-=[Che68]-=-: Assume (AXsB) is the system of inequalities of a polyhedron P . A system of generators of P can be computed iteratively as follows: Start with P 0 = jj Q n , the whole space, a system of generators ... |

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4 |
Model-checking strategies for hybrid systems. Presented at the
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Citation Context ...ows the available operations to be interactively invoked. A prototype analyzer of hybrid automata. Automata are described in a hybrid extension of the Argos formalism [Mar92]. 3 For the same example, =-=[HH94]-=- solves the problem by changing the control structure of the automaton, by distinguishing the locations according to the values of k1 and k2 . They get exact results, but of course, such a change in t... |