Related papers: Craig Interpolation in Program Verification

This paper introduces a new framework for constructing the Discrete Empirical Interpolation Method DEIM projection operator. The interpolation node selection procedure is formulated using the QR factorization with column pivoting, and it…

Program transformation is an appealing technique which allows to improve run-time efficiency, space-consumption and more generally to optimize a given program. Essentially it consists of a sequence of syntactic program manipulations which…

Used to estimate the risk of an estimator or to perform model selection, cross-validation is a widespread strategy because of its simplicity and its apparent universality. Many results exist on the model selection performances of…

The problem of computing Craig interpolants in SAT and SMT has recently received a lot of interest, mainly for its applications in formal verification. Efficient algorithms for interpolant generation have been presented for some theories of…

We show that Propositional Dynamic Logic (PDL) has the Craig Interpolation Property. This question has been open for many years. Three proof attempts were published, but later criticized in the literature or retracted. Our proof is based on…

Verifying multi-threaded programs is becoming more and more important, because of the strong trend to increase the number of processing units per CPU socket. We introduce a new configurable program analysis for verifying multi-threaded…

These notes outline a formal method for program verification of numerical computation. It forms the basis of the software package VPC in its initial phase of development. Much of the style of presentation is in the form of notes that…

Arithmetic complexity has a main role in the performance of algorithms for spectrum evaluation. Arithmetic transform theory offers a method for computing trigonometrical transforms with minimal number of multiplications. In this paper, the…

Common model selection criteria, such as $AIC$ and its variants, are based on in-sample prediction error estimators. However, in many applications involving predicting at interpolation and extrapolation points, in-sample error cannot be…

The automation offered by modern program proof tools goes hand in hand with the capability to interact with the tool when the verification fails. The SPARK proof tool tries to help the user by providing the right information, so that the…

A C++ software design is presented that can be used to interpolate data in any number of dimensions. The design is based on a combination of templates of functional collections of elements and so-called type lists. The design allows for…

When methods of moments are used for identification of power spectral densities, a model is matched to estimated second order statistics such as, e.g., covariance estimates. If the estimates are good there is an infinite family of power…

This article examines two approaches to verification, one based on using a logic for expressing properties of a system, and one based on showing the system equivalent to a simpler system that obviously has whatever property is of interest.…

Integer overflow accounts for one of the major source of bugs in software. Verification systems typically assume a well defined underlying semantics for various integer operations and do not explicitly check for integer overflow in…

The Empirical Interpolation Method (EIM) is a greedy procedure that constructs approximate representations of two-variable functions in separated form. In its classical presentation, the two variables play a non-symmetric role. In this…

In this paper, we outline an approach to verifying parallel programs. A new mathematical model of parallel programs is introduced. The introduced model is illustrated by the verification of the matrix multiplication MPI program.

Several techniques and tools have been developed for verification of properties expressed as Horn clauses with constraints over a background theory (CHC). Current CHC verification tools implement intricate algorithms and are often limited…

Couplings are a powerful mathematical tool for reasoning about pairs of probabilistic processes. Recent developments in formal verification identify a close connection between couplings and pRHL, a relational program logic motivated by…

The verification of multithreaded software is still a challenge. This comes mainly from the fact that the number of thread interleavings grows exponentially in the number of threads. The idea that thread interleavings can be studied with a…

This paper describes the formal verification of two Turing machines using the program verifier Dafny. Both machines are deciders, so we prove total correctness. They are typical first examples of Turing machines used in any course of…