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A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g.,…
Designing large-scale control systems to satisfy complex specifications is hard in practice, as most formal methods are limited to systems of modest size. Contract theory has been proposed as a modular alternative to formal methods in…
In this work, we introduce a compositional framework for the construction of finite abstractions (a.k.a. symbolic models) of interconnected discrete-time control systems. The compositional scheme is based on the joint dissipativity-type…
Figuring out the physical rationale behind natural selection of quantum theory is one of the most acclaimed quests in quantum foundational research. This pursuit has inspired several axiomatic initiatives to derive mathematical formulation…
Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization CL18 of the basic propositional fragment of computability…
This article is intended to an introductory lecture in material physics, in which the modern computational group theory and the electronic structure calculation are in collaboration. The effort of mathematicians in field of the group…
Chemical systems are traditionally described by lists of species, reactions, and externally imposed kinetic laws, a framework that lacks an intrinsic algebraic structure governing how transformations compose. We propose an axiomatic…
Multivariate information theory provides a general and principled framework for understanding how the components of a complex system are connected. Existing analyses are coarse in nature -- built up from characterizations of discrete…
Cyber-physical systems (CPSs) embed software into the physical world. They appear in a wide range of applications such as smart grids, robotics, intelligent manufacture and medical monitoring. CPSs have proved resistant to modeling due to…
In this work we present an intuitive construction of the quantum logical axiomatic system provided by George Mackey. The goal of this work is a detailed discussion of the results from the paper 'Physical justification for using the tensor…
The aim of this paper is to propose an alternative behavioural definition of computation (and of a computer) based simply on whether a system is capable of reacting to the environment-the input-as reflected in a measure of programmability.…
In the paper we present results to develop an irreducible theory of complex systems in terms of self-organization processes of prime integer relations. Based on the integers and controlled by arithmetic only the self-organization processes…
Accountability is the property of a system that enables the uncovering of causes for events and helps understand who or what is responsible for these events. Definitions and interpretations of accountability differ; however, they are…
In this paper, we propose a compositional approach to construct opacity-preserving finite abstractions (a.k.a symbolic models) for networks of discrete-time nonlinear control systems. Particularly, we introduce new notions of simulation…
Temporal logics stands for a widely adopted family of formalisms for the verification of computational devices, enriching propositional logics by operators predicating on the step-wise behaviour of a system. Its quantified extensions allow…
This paper presents an investigation of the notion of reaction time in some synchronous systems. A state-based description of such systems is given, and the reaction time of such systems under some classic composition primitives is studied.…
This book explores an alternative to the current dominant paradigm where a discrete computer model is constructed as an attempt to approximate some continuum theory. We focus on a class of discrete computer models that are based on simple…
We propose a process calculus, named AbC, to study the behavioural theory of interactions in collective-adaptive systems by relying on attribute-based communication. An AbC system consists of a set of parallel components each of which is…
Sets of equations E play an important computational role in rewriting-based systems R by defining an equivalence relation =E inducing a partition of terms into E-equivalence classes on which rewriting computations, denoted ->R/E and called…
We provide an overview of a canonical formalism that describes mixed quantum-classical systems in terms of statistical ensembles on configuration space, and discuss applications to measurement theory. It is shown that the formalism allows a…