95,645 research outputs found
Data-driven Abstractions for Verification of Deterministic Systems
A common technique to verify complex logic specifications for dynamical
systems is the construction of symbolic abstractions: simpler, finite-state
models whose behaviour mimics the one of the systems of interest. Typically,
abstractions are constructed exploiting an accurate knowledge of the underlying
model: in real-life applications, this may be a costly assumption. By sampling
random -step trajectories of an unknown system, we build an abstraction
based on the notion of -completeness. We newly define the notion of
probabilistic behavioural inclusion, and provide probably approximately correct
(PAC) guarantees that this abstraction includes all behaviours of the concrete
system, for finite and infinite time horizon, leveraging the scenario theory
for non convex problems. Our method is then tested on several numerical
benchmarks
An Effective Fixpoint Semantics for Linear Logic Programs
In this paper we investigate the theoretical foundation of a new bottom-up
semantics for linear logic programs, and more precisely for the fragment of
LinLog that consists of the language LO enriched with the constant 1. We use
constraints to symbolically and finitely represent possibly infinite
collections of provable goals. We define a fixpoint semantics based on a new
operator in the style of Tp working over constraints. An application of the
fixpoint operator can be computed algorithmically. As sufficient conditions for
termination, we show that the fixpoint computation is guaranteed to converge
for propositional LO. To our knowledge, this is the first attempt to define an
effective fixpoint semantics for linear logic programs. As an application of
our framework, we also present a formal investigation of the relations between
LO and Disjunctive Logic Programming. Using an approach based on abstract
interpretation, we show that DLP fixpoint semantics can be viewed as an
abstraction of our semantics for LO. We prove that the resulting abstraction is
correct and complete for an interesting class of LO programs encoding Petri
Nets.Comment: 39 pages, 5 figures. To appear in Theory and Practice of Logic
Programmin
Synthesizing Short-Circuiting Validation of Data Structure Invariants
This paper presents incremental verification-validation, a novel approach for
checking rich data structure invariants expressed as separation logic
assertions. Incremental verification-validation combines static verification of
separation properties with efficient, short-circuiting dynamic validation of
arbitrarily rich data constraints. A data structure invariant checker is an
inductive predicate in separation logic with an executable interpretation; a
short-circuiting checker is an invariant checker that stops checking whenever
it detects at run time that an assertion for some sub-structure has been fully
proven statically. At a high level, our approach does two things: it statically
proves the separation properties of data structure invariants using a static
shape analysis in a standard way but then leverages this proof in a novel
manner to synthesize short-circuiting dynamic validation of the data
properties. As a consequence, we enable dynamic validation to make up for
imprecision in sound static analysis while simultaneously leveraging the static
verification to make the remaining dynamic validation efficient. We show
empirically that short-circuiting can yield asymptotic improvements in dynamic
validation, with low overhead over no validation, even in cases where static
verification is incomplete
Observational Equivalence and Full Abstraction in the Symmetric Interaction Combinators
The symmetric interaction combinators are an equally expressive variant of
Lafont's interaction combinators. They are a graph-rewriting model of
deterministic computation. We define two notions of observational equivalence
for them, analogous to normal form and head normal form equivalence in the
lambda-calculus. Then, we prove a full abstraction result for each of the two
equivalences. This is obtained by interpreting nets as certain subsets of the
Cantor space, called edifices, which play the same role as Boehm trees in the
theory of the lambda-calculus
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
The abstraction effect on logic rules application
The aim of this study is to analyze the relationship between training on abstraction and the comprehension of logic rules. In order to evaluate the possibility of improvement on logic performance we have selected the particular case of the DeMorgan’s laws. The dispute between the natural logic approach and the mental models theory is analyzed from the perspective of such abstraction effect. Two experiments are reported. The first one suggests that the presentation of a formal proof promotes a better comprehension of DeMorgan´s laws than the use of visual resources or colloquial examples. The second one offers a stronger test for the same abstraction effect. Some limitations concerned with the syntactic meaning of negation and the differences between constructive and evaluative conditions are discussed. Since the meaning of abstraction for the psychology of reasoning is pointed out as critical some suggestions for further research and possible educational applications are mentioned.Fil: Macbeth, Guillermo Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Entre Ríos. Facultad de Ciencias de la Educación; ArgentinaFil: Razumiejczyk, Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Entre Ríos. Facultad de Ciencias de la Educación; ArgentinaFil: Campitelli, Guillermo Jorge. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Edith Cowan University; Australi
Modal logics for reasoning about object-based component composition
Component-oriented development of software supports the adaptability and maintainability of large systems, in particular if requirements change over time and parts of a system have to be modified or replaced. The software architecture in such systems can be described by components
and their composition. In order to describe larger architectures, the composition concept becomes crucial. We will present a formal framework for component composition for object-based software development. The deployment of modal logics for defining components and component composition will allow us to reason about and prove properties of components and compositions
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