Related papers: Invariant Checking for SMT-based Systems with Quan…
Automatic verification of concurrent programs faces state explosion due to the exponential possible interleavings of its sequential components coupled with large or infinite state spaces. An alternative is deductive verification, where…
Confluence denotes the property of a state transition system that states can be rewritten in more than one way yielding the same result. Although it is a desirable property, confluence is often too strict in practical applications because…
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…
We present an automated compositional program verification technique for safety properties based on conditional inductive invariants. For a given program part (e.g., a single loop) and a postcondition $\varphi$, we show how to, using a…
Bargmann invariants of order $n$, defined as multivariate traces of quantum states $\text{Tr}[\rho_1\rho_2 \ldots \rho_n]$, are useful in applications ranging from quantum metrology to certification of nonclassicality. A standard quantum…
The biggest challenge in hybrid systems verification is the handling of differential equations. Because computable closed-form solutions only exist for very simple differential equations, proof certificates have been proposed for more…
Model-based mutation testing uses altered test models to derive test cases that are able to reveal whether a modelled fault has been implemented. This requires conformance checking between the original and the mutated model. This paper…
The invariant filtering theory based on the group theory has been successful in statistical filtering methods. However, there exists a class of state estimation problems with unknown statistical properties of noise disturbances, and it is…
The invariant classification of superintegrable systems is reviewed and utilized to construct singular limits between the systems. It is shown, by construction, that all superintegrable systems on conformally flat, 3D complex Riemannian…
This paper deals with the problem of state estimation for a class of linear time-invariant systems with quadratic output measurements. An immersion-type approach is presented that transforms the system into a state-affine system by adding a…
We study model checking algorithms for infinite families of finite-state labeled transition systems against temporal properties written in CTL*. Such families arise, for example, as models of highly configurable systems or software product…
We study a class of Markov chains that model the evolution of a quantum system subject to repeated measurements. Each Markov chain in this class is defined by a measure on the space of matrices. It is then given by a random product of…
The invariant measure is a fundamental object in the theory of Markov processes. In finite dimensions a Markov process is defined by transition rates of the corresponding stochastic matrix. The Markov tree theorem provides an explicit…
Two pretrained neural networks are deemed equivalent if they yield similar outputs for the same inputs. Equivalence checking of neural networks is of great importance, due to its utility in replacing learning-enabled components with…
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…
Ensuring software correctness remains a fundamental challenge in formal program verification. One promising approach relies on finding polynomial invariants for loops. Polynomial invariants are properties of a program loop that hold before…
We consider the stability and the input-output analysis problems of a class of large-scale hybrid systems composed of continuous dynamics coupled with discrete dynamics defined over finite alphabets, e.g., deterministic finite state…
We give an algorithm allowing to construct bases of local unitary invariants of pure k-qubit states from the knowledge of polynomial covariants of the group of invertible local filtering operations. The simplest invariants obtained in this…
The goal of invariant theory is to find all the generators for the algebra of representations of a group that leave the group invariant. Such generators will be called \emph{basic invariants}. In particular, we set out to find the set of…
In previous work, we presented a symbolic execution method which starts with a concrete model of the program but progressively abstracts away details only when these are known to be irrelevant using interpolation. In this paper, we extend…