P. Cousot. Mthodes itratives de construction et d'approximation de point xes d'oprateurs monotones sur un treillis, analyse smantique des programmes. Thse s sciences mathmatiques, University of Grenoble, March 1978. Home/Search Document Not in Database Summary Related Articles Check |
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Assertion-Based Debugging of Imperative Programs By Interpretation - Bourdoncle (1993) (1 citation) (Correct)
....all the bugs in a program is undecidable, we introduce in this paper an assertionbased framework that enables the static and automatic discovery of certain categories of bugs. This framework is based on abstract interpretation, which is a formal method, pioneered by Patrick and Radhia Cousot [7, 10, 12], that enables the static and automatic determination of safe and approximate run time properties of programs. So far, abstract interpretation has mainly been used in compilers to optimize, vectorize, determine the lifetime of dynamically allocated data structures (compile time garbage ....
....variable i are always less than 100. Of course, the method we have described is interesting from a mathematical point of view, but is not directly implementable, since fixed points over infinite domains are not computable in general. This is why abstract interpretation defines standard methods [3, 4, 5, 6, 7, 10, 11, 12] for finitely and iteratively computing safe approximations of I. These approximate invariants I # describe true properties about the run time behavior of the program, that is I ) I # , but are not necessarily optimal. Note that if the approximation of the program invariant I is necessary for ....
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Patrick Cousot: "Mthodes itratives de construction et d'approximation de points fixes d'oprateurs monotones sur un treillis. Analyse smantique de programmes", Ph. D. dissertation, Universit Scientifique et Mdicale de Grenoble (1978)
Verification of Embedded Software: Problems and Perspectives - Cousot, Cousot (2001) (1 citation) Self-citation (Cousot) (Correct)
....chain conditions do require the use of widening narrowing techniques [29, 30] in order to accelerate the convergence of fixpoint computations into ap# proximations from above or to choose among alternatives in absence of a best approximation. Dual notions do exist for approximations from below [23]. Widen# ing narrowing techniques are also used in model checking although the link with these well known techniques is not always recognized (e.g. compare the widening for BDDs of [66] to that of [71] The widening narrowing technique is a dynamic approximation technique (during fixpoint ....
P. Cousot. Mthodes itratives de construction et d'approximation de points fixes d'oprateurs monotones sur un treillis, analyse smantique de programmes. Thse d'tat s sciences mathmatiques, Universit scientifique et mdicale de Grenoble, Grenoble, FR, 21 Mar. 1978.
Modular Static Program Analysis - Cousot, Cousot (2002) (8 citations) Self-citation (Cousot) (Correct)
....more precise analyzes of the parts. Since these separate analyzes can be performed in parallel on independent computers, the global program analysis time may also reduced. 2 Global Static Program Analysis The formulation of global static program analysis in the abstract interpretation framework [11, 16, 17, 21] consists in computing an approximation of a program semantics expressing the properties of interest of the program P to be analyzed. The semantics can often be expressed as a least xpoint that is as the least solution to a monotonic system of equations X = F computed on a poset where ....
....through a Galois connection ## # # # where a concrete program property p D is approximated by any abstract program property p D such that p #(p) and has a best more precise abstraction #(p) D (Other formalizations through closure operators, ideals, etc. are equivalent [11, 21]. The best abstraction hypothesis can also be relaxed [24] Then global static program analysis consists in computing an abstract least xpoint which is a sound approximation of the concrete semantics in that lfp #(lfp #P #) This xpoint soundness condition can be ensured ....
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P. Cousot. Mthodes itratives de construction et d'approximation de points xes d'oprateurs monotones sur un treillis, analyse smantique de programmes. Thse d'tat s sciences mathmatiques, Universit scientique et mdicale de Grenoble, 21 Mar. 1978.
On Abstraction in Software Verification - Cousot, Cousot (2002) Self-citation (Cousot) (Correct)
....of temporal logic based verification methods [1, 2] The purpose of this paper is to discuss the practical importance of this abstraction when designing static software checking algorithms. This is illustrated on reachability analysis and abstract testing. 2 Transition Systems We follow [3, 4] in formalizing a hardware or software computer system by a transition system xS, t, I , F, Ey with set of states S, transition relation t # pS Sq, initial states I # S, erroneous states E # S, and final states F # S. An example is that of automatic program manipulation techniques based on the ....
.... are reachable from a state of X by a transition t: postrts X P S Ds P X : xs, s y P tu [5, 6] Let # be the least fixpoint of a monotone map # on a poset xL, #y when it exists (e.g. xL, #y is a cpo or a complete lattice) We have postrt s I lfp FrtsIpXq I Y postrts X [3, 5]. Given a specification Q # S, the reachability problem considered in [5] consists in proving that postrt s I # Q. Inverse problems consist in considering the inverse t of the relation t [3] We let prerts X postrt s X be the pre image of X by t that is the set of states from which ....
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Cousot, P.: Mthodes itratives de construction et d'approximation de points fixes d'oprateurs monotones sur un treillis, analyse smantique de programmes. Thse d'tat s sciences mathmatiques, Universit scientifique et mdicale de Grenoble, Grenoble, France (1978)
Refining Model Checking by Abstract Interpretation - Cousot, Cousot (1999) (5 citations) Self-citation (Cousot) (Correct)
....finite transition systems can be simply extended to the infinite case. One can use abstract interpretation techniques such as widening and narrowing to enforce, on the fly, the convergence of fixpoint computations. It is known in abstract interpretation that this is not as precise as could it be (Cousot, 1978, Cousot and Cousot, 1992a) Hence we propose a combination of forward and backward upper approximate universal safety checking which is more precise than the mere conjunction of these forward and backward analyses (which are indeed equivalent for finite states) We also suggest another possible ....
....s # ##t . The dual post image # post[t] P is the set of states which can only be reached, if ever possible, by a transition t from P: # post[t] P # =post[t] P) s # #s : #s, s # ##t ## s # P . This is illustrated in Figure 2. We have the fixpoint characterizations (see e.g. (Cousot, 1978), Cousot, 1981) REFINING MODEL CHECKING 73 pre[t # ] F = lfp # #X . F # pre[t] X = lfp # F #X . X # pre[t] X, # pre[t # ] F = gfp # #X . F # # pre[t] X = gfp # F #X . X # # pre[t] X, post[t # ] I = lfp # #X . I # post[t] X = lfp # I #X ....
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Cousot, P. 1978. Mthodes itratives de construction et d'approximation de points fixes d'oprateurs monotones sur un treillis, analyse smantique de programmes. Ph. D. thesis, Universit scientifique et mdicale de Grenoble, Grenoble, FRA.
Combining Forward And Backward Analyses Of Temporal Properties - Masse (2001) (Correct)
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P. Cousot. Mthodes itratives de construction et d'approximation de point xes d'oprateurs monotones sur un treillis, analyse smantique des programmes. Thse s sciences mathmatiques, University of Grenoble, March 1978.
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