Related papers: The Structure of Differential Invariants and Diffe…
Automated program verification often proceeds by exhibiting inductive invariants entailing the desired properties.For numerical properties, a classical class of invariants is convex polyhedra: solution sets of system of linear…
Invariants are the predominant approach to verify the correctness of loops. As an alternative, loop contracts, which make explicit the premise and conclusion of the underlying induction proof, can sometimes capture correctness conditions…
Software model checking is a challenging problem, and generating relevant invariants is a key factor in proving the safety properties of a program. Program invariants can be obtained by various approaches, including lightweight procedures…
The persistence barcode (equivalently, the persistence diagram), which can be obtained from the interval decomposition of a persistence module, plays a pivotal role in applications of persistent homology. For multi-parameter persistent…
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…
Termination analysis of linear loops plays a key r\^{o}le in several areas of computer science, including program verification and abstract interpretation. Already for the simplest variants of linear loops the question of termination…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construc-tion uses a single linear differential form defined from the…
Invariants of general linear system of two hyperbolic partial differential equations (PDEs) are derived under transformations of the dependent and independent variables by real infinitesimal method earlier. Here a subclass of the general…
It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a…
Barrier certificates, a form of state invariants, provide an automated approach to the verification of the safety of dynamical systems. Similarly to barrier certificates, recent works explore the notion of closure certificates, a form of…
Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…
This paper addresses the problem of checking invariant properties for a large class of symbolic transition systems, defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort…
The reliability and proper function of data-driven applications hinge on the data's continued conformance to the applications' initial design. When data deviates from this initial profile, system behavior becomes unpredictable. Data…
Mathematical proofs are a cornerstone of control theory, and it is important to get them right. Deduction systems can help with this by mechanically checking the proofs. However, the structure and level of detail at which a proof is…
Cut-elimination is the bedrock of proof theory with a multitude of applications from computational interpretations to proof analysis. It is also the starting point for important meta-theoretical investigations including decidability,…
In [1], we have presented the theoretical background for finding the Elementary Invariants for a 3D system of first order rational differential equations (1ODEs). We have also provided an algorithm to find such Invariants. Here we introduce…
Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, making the CAD invariant with…
In the identification of differential equations from data, significant progresses have been made with the weak/integral formulation. In this paper, we explore the direction of finding more efficient and robust test functions adaptively…
This paper introduces an inner product on chain complexes of finite simplicial complexes that is well-adapted to the harmonic study of subdivisions. Its definition utilizes a decomposition of the chain spaces that suggests a sequence of…