Abstract interpretation paper

The dependency semantics, derived by abstraction of the trace semantics, is sound and complete for data usage.

abstract domain meaning

Compared to current analysis methods, the responsibility analysis is more precise. These two sets are related to each other by defining total functions that map elements from one to the other.

While each of the operations taken individually was exactly abstracted, their composition isn't.

Abstract interpretation past present and future

We survey existing analyses and identify key design decisions that limit or facilitate their applicability to input data usage, and we assess their precision. A state assigning the value v x to variable x will be a concretization of these intervals if for all x, v x is in [Lx, Hx]. The goal of static analysis is to derive a computable semantic interpretation at some point. Let us suppose that L is a complete lattice and let f be a monotonic function from L into L. In this paper, a novel definition of responsibility based on the abstraction of event trace semantics is proposed, which can be applied in program security and other scientific fields. Formal Methods Formal methods are abstract interpretations which differ in the way the abstract semantics is obtained. Briefly speaking, an entity ER is responsible for behavior B, if and only if ER is free to choose its input value, and such a choice is the first one that ensures the occurrence of B in the forthcoming execution. In deductive methods the abstract semantics is specified by verification conditions and must be provided by the user in the form of inductive properties true at each program step, such as loop invariants satisfying these verification conditions [ 5 ]. Authors: Chaoqiang Deng , Patrick Cousot Submitted on 18 Jul Abstract: Given a behavior of interest in the program, statically determining the corresponding responsible entity is a task of critical importance, especially in program security. Our notion of dependency accounts for non-determinism and non-termination.

In model-checking, the abstract semantics is provided manually by the user in the form of a finitary model of the program execution for example a finite automaton [ 9 ].

In static analysis, the abstract semantics is computed automatically thanks to predefined approximations [ 1678 ], possibly manually parameterizable by the user.

Abstract interpretation art

This is the same problem of absence of coverage. If the person we are looking up is a criminal, we will issue an alarm; but there is of course the possibility of issuing a false alarm. Some examples of relational numerical abstract domains are:. More abstract semantics are then derived; for instance, one may consider only the set of reachable states in the executions which amounts to considering the last states in finite traces. Otherwise, we may only be able to say that we do not know. Abstract Interpretation Abstract interpretation consists in considering an abstract semantics, that is a superset of the concrete program semantics: x t t The abstract semantics covers all possible cases. Finally, we demonstrate the value of expressing such analyses as abstract interpretation by combining them with an existing abstraction of compound data structures such as arrays and lists to detect unused chunks of the data. We show that non-interference analyses [ 6 ] are sound for proving that a terminating program does not use any of its input data; although this is too strong a property in general. In practice the abstractions that are defined are tailored to both the program properties one desires to analyze, and to the set of target programs. If this is already too much to handle, we might keep only the age of the youngest, m and oldest person, M. Non-relational domains tend to be fast and simple to implement, but imprecise. Part of the Lecture Notes in Computer Science book series LNCS, volume Abstract Data science software plays an increasingly important role in critical decision making in fields ranging from economy and finance to biology and medicine. Concrete semantics of programs The concrete semantics of programs formalizes the set of all possible executions of this program in all possible execution environments.

Part of the Lecture Notes in Computer Science book series LNCS, volume Abstract Data science software plays an increasingly important role in critical decision making in fields ranging from economy and finance to biology and medicine.

Whence, if the abstract semantics is safe i.

abstract interpretation compiler
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An Abstract Interpretation Framework for Input Data Usage