407 research outputs found
Succinct Representations for Abstract Interpretation
Abstract interpretation techniques can be made more precise by distinguishing
paths inside loops, at the expense of possibly exponential complexity.
SMT-solving techniques and sparse representations of paths and sets of paths
avoid this pitfall. We improve previously proposed techniques for guided static
analysis and the generation of disjunctive invariants by combining them with
techniques for succinct representations of paths and symbolic representations
for transitions based on static single assignment. Because of the
non-monotonicity of the results of abstract interpretation with widening
operators, it is difficult to conclude that some abstraction is more precise
than another based on theoretical local precision results. We thus conducted
extensive comparisons between our new techniques and previous ones, on a
variety of open-source packages.Comment: Static analysis symposium (SAS), Deauville : France (2012
Splitting Proofs for Interpolation
We study interpolant extraction from local first-order refutations. We
present a new theoretical perspective on interpolation based on clearly
separating the condition on logical strength of the formula from the
requirement on the com- mon signature. This allows us to highlight the space of
all interpolants that can be extracted from a refutation as a space of simple
choices on how to split the refuta- tion into two parts. We use this new
insight to develop an algorithm for extracting interpolants which are linear in
the size of the input refutation and can be further optimized using metrics
such as number of non-logical symbols or quantifiers. We implemented the new
algorithm in first-order theorem prover VAMPIRE and evaluated it on a large
number of examples coming from the first-order proving community. Our
experiments give practical evidence that our work improves the state-of-the-art
in first-order interpolation.Comment: 26th Conference on Automated Deduction, 201
A Reduction from Unbounded Linear Mixed Arithmetic Problems into Bounded Problems
We present a combination of the Mixed-Echelon-Hermite transformation and the
Double-Bounded Reduction for systems of linear mixed arithmetic that preserve
satisfiability and can be computed in polynomial time. Together, the two
transformations turn any system of linear mixed constraints into a bounded
system, i.e., a system for which termination can be achieved easily. Existing
approaches for linear mixed arithmetic, e.g., branch-and-bound and cuts from
proofs, only explore a finite search space after application of our two
transformations. Instead of generating a priori bounds for the variables, e.g.,
as suggested by Papadimitriou, unbounded variables are eliminated through the
two transformations. The transformations orient themselves on the structure of
an input system instead of computing a priori (over-)approximations out of the
available constants. Experiments provide further evidence to the efficiency of
the transformations in practice. We also present a polynomial method for
converting certificates of (un)satisfiability from the transformed to the
original system
Екатеринбургская неделя. 1883. № 50
This is the author’s accepted manuscript. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-24364-6_12.acmid: 2050798 location: Saarbrücken, Germany numpages: 16acmid: 2050798 location: Saarbrücken, Germany numpages: 1
A Simplex-Based Extension of Fourier-Motzkin for Solving Linear Integer Arithmetic
International audienceThis paper describes a novel decision procedure for quantifier-free linear integer arithmetic. Standard techniques usually relax the initial problem to the rational domain and then proceed either by projection (e.g. Omega-Test) or by branching/cutting methods (branch-and-bound, branch-and-cut, Gomory cuts). Our approach tries to bridge the gap between the two techniques: it interleaves an exhaustive search for a model with bounds inference. These bounds are computed provided an oracle capable of finding constant positive linear combinations of affine forms. We also show how to design an efficient oracle based on the Simplex procedure. Our algorithm is proved sound, complete, and terminating and is implemented in the Alt-Ergo theorem prover. Experimental results are promising and show that our approach is competitive with state-of-the-art SMT solvers
Computation of the Transient in Max-Plus Linear Systems via SMT-Solving
This paper proposes a new approach, grounded in Satisfiability Modulo
Theories (SMT), to study the transient of a Max-Plus Linear (MPL) system, that
is the number of steps leading to its periodic regime. Differently from
state-of-the-art techniques, our approach allows the analysis of periodic
behaviors for subsets of initial states, as well as the characterization of
sets of initial states exhibiting the same specific periodic behavior and
transient. Our experiments show that the proposed technique dramatically
outperforms state-of-the-art methods based on max-plus algebra computations for
systems of large dimensions.Comment: The paper consists of 22 pages (including references and Appendix).
It is accepted in FORMATS 2020 First revisio
Square root and division elimination in PVS
International audienceIn this paper we present a new strategy for PVS that imple- ments a square root and division elimination in order to use automatic arithmetic strategies that were not able to deal with these operations in the ﰁrst place. This strategy relies on a PVS formalization of the square root and division elimination and deep embedding of PVS expressions inside PVS. Therefore using computational reﰂection and symbolic com- putation we are able to automatically transform expressions into division and square root free ones before using these decision procedures
Formalising the Continuous/Discrete Modeling Step
Formally capturing the transition from a continuous model to a discrete model
is investigated using model based refinement techniques. A very simple model
for stopping (eg. of a train) is developed in both the continuous and discrete
domains. The difference between the two is quantified using generic results
from ODE theory, and these estimates can be compared with the exact solutions.
Such results do not fit well into a conventional model based refinement
framework; however they can be accommodated into a model based retrenchment.
The retrenchment is described, and the way it can interface to refinement
development on both the continuous and discrete sides is outlined. The approach
is compared to what can be achieved using hybrid systems techniques.Comment: In Proceedings Refine 2011, arXiv:1106.348
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