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The role of the observers is frequently obscured in the literature, either by writing equations in a coordinate system implicitly pertaining to some specific observer or by entangling the invariance and the observer dependence of physical…
Our aim is to statically verify that in a given reactive program, the length of collection variables does not grow beyond a given bound. We propose a scalable type-based technique that checks that each collection variable has a given…
The Astr\'{e}e static analyzer is a specialized tool that can prove the absence of runtime errors, including arithmetic overflows, in large critical programs. Keeping analysis times reasonable for industrial use is one of the design…
Static code analysis (SCA) tools are widely used as effective ways to detect bugs and vulnerabilities in software systems. However, the reports generated by these tools often contain a large number of non-actionable findings, which can…
We determine the boundedness and compactness of a large class of operators, mapping from general Banach spaces of holomorphic functions into a particular type of spaces of functions determined by the growth of the functions, or the growth…
If the result of an expensive computation is invalidated by a small change to the input, the old result should be updated incrementally instead of reexecuting the whole computation. We incrementalize programs through their derivative. A…
Linear Time Invariant (LTI) systems are ubiquitous in control applications. Unbounded-time reachability analysis that can cope with industrial-scale models with thousands of variables is needed. To tackle this problem, we use abstract…
Multivariate Analysis is an increasingly common tool in experimental high energy physics; however, many of the common approaches were borrowed from other fields. We clarify what the goal of a multivariate algorithm should be for the search…
We consider the problem of formalizing the familiar notion of widening in abstract interpretation in higher-order logic. It turns out that many axioms of widening (e.g. widening sequences are ascending) are not useful for proving…
Processes occurring in real open systems are far from equilibrium state and they can lead to synergetic effects, which are caused by coordinated behavior of system units. Traditional methods of analysis often just establish such behavior,…
In this paper, we apply the recently developed generalized parameter estimation-based observer design technique for state-affine systems to the practically important case of linear time-varying descriptor systems with uncertain parameters.…
We consider regression in which one predicts a response $Y$ with a set of predictors $X$ across different experiments or environments. This is a common setup in many data-driven scientific fields and we argue that statistical inference can…
Just like other software, spreadsheets can contain significant faults. Static analysis is an accepted and well-established technique in software engineering known for its capability to discover faults. In recent years, a growing number of…
In this paper, we study infinite dimensional stochastic systems having both unbounded control and observation operators. First of all, using a semigroup approach, we give another take of the well-posedness of such systems treated in [SIAM…
We present and evaluate a technique for computing path-sensitive interference conditions during abstract interpretation of concurrent programs. In lieu of fixed point computation, we use prime event structures to compactly represent causal…
We extend the definition of generalized coherent states to include the case of time-dependent dispersion. We introduce a suitable operator providing displacement and dynamical rescaling from an arbitrary ground state. As a consequence,…
We present a logic for the specification of static analysis problems that goes beyond the logics traditionally used. Its most prominent feature is the direct support for both inductive computations of behaviors as well as co-inductive…
We consider a class of uncertain linear time-invariant overparametrized systems affected by bounded disturbances, which are described by a known exosystem with unknown initial conditions. For such systems an exponentially stable extended…
Decidability and synthesis of inductive invariants ranging in a given domain play an important role in many software and hardware verification systems. We consider here inductive invariants belonging to an abstract domain $A$ as defined in…
The identification of slow invariant manifolds (SIMs) is an essential part in model-order reduction for reactive systems. The mathematical definition of the SIM by Fenichel can be considered unsatisfactory, because it is only applicable to…