25,066 research outputs found
Constraint-Based Qualitative Simulation
We consider qualitative simulation involving a finite set of qualitative
relations in presence of complete knowledge about their interrelationship. We
show how it can be naturally captured by means of constraints expressed in
temporal logic and constraint satisfaction problems. The constraints relate at
each stage the 'past' of a simulation with its 'future'. The benefit of this
approach is that it readily leads to an implementation based on constraint
technology that can be used to generate simulations and to answer queries about
them.Comment: 10 pages, to appear at the conference TIME 200
Instantiation of SMT problems modulo Integers
Many decision procedures for SMT problems rely more or less implicitly on an
instantiation of the axioms of the theories under consideration, and differ by
making use of the additional properties of each theory, in order to increase
efficiency. We present a new technique for devising complete instantiation
schemes on SMT problems over a combination of linear arithmetic with another
theory T. The method consists in first instantiating the arithmetic part of the
formula, and then getting rid of the remaining variables in the problem by
using an instantiation strategy which is complete for T. We provide examples
evidencing that not only is this technique generic (in the sense that it
applies to a wide range of theories) but it is also efficient, even compared to
state-of-the-art instantiation schemes for specific theories.Comment: Research report, long version of our AISC 2010 pape
Modular Construction of Shape-Numeric Analyzers
The aim of static analysis is to infer invariants about programs that are
precise enough to establish semantic properties, such as the absence of
run-time errors. Broadly speaking, there are two major branches of static
analysis for imperative programs. Pointer and shape analyses focus on inferring
properties of pointers, dynamically-allocated memory, and recursive data
structures, while numeric analyses seek to derive invariants on numeric values.
Although simultaneous inference of shape-numeric invariants is often needed,
this case is especially challenging and is not particularly well explored.
Notably, simultaneous shape-numeric inference raises complex issues in the
design of the static analyzer itself.
In this paper, we study the construction of such shape-numeric, static
analyzers. We set up an abstract interpretation framework that allows us to
reason about simultaneous shape-numeric properties by combining shape and
numeric abstractions into a modular, expressive abstract domain. Such a modular
structure is highly desirable to make its formalization and implementation
easier to do and get correct. To achieve this, we choose a concrete semantics
that can be abstracted step-by-step, while preserving a high level of
expressiveness. The structure of abstract operations (i.e., transfer, join, and
comparison) follows the structure of this semantics. The advantage of this
construction is to divide the analyzer in modules and functors that implement
abstractions of distinct features.Comment: In Proceedings Festschrift for Dave Schmidt, arXiv:1309.455
- …