The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Recursion theory on the reals and continuous-time computation
Theoretical Computer Science - Special issue on real numbers and computers
Complexity and real computation
Complexity and real computation
Mathematical control theory: deterministic finite dimensional systems (2nd ed.)
Mathematical control theory: deterministic finite dimensional systems (2nd ed.)
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Concurrent Systems: An Integrated Approach to Operating Systems, Database, and Distributed ...
Concurrent Systems: An Integrated Approach to Operating Systems, Database, and Distributed ...
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Specifying Systems: The TLA+ Language and Tools for Hardware and Software Engineers
Specifying Systems: The TLA+ Language and Tools for Hardware and Software Engineers
Theory of Modeling and Simulation
Theory of Modeling and Simulation
Theoretical Computer Science
Abstract State Machines: A Method for High-Level System Design and Analysis
Abstract State Machines: A Method for High-Level System Design and Analysis
Verification of Reactive Systems: Formal Methods and Algorithms
Verification of Reactive Systems: Formal Methods and Algorithms
Embedded Systems Handbook
Embedded System Design
Modelling of complex software systems: a reasoned overview
FORTE'06 Proceedings of the 26th IFIP WG 6.1 international conference on Formal Techniques for Networked and Distributed Systems
Understanding Basic Automata Theory in the Continuous Time Setting
Fundamenta Informaticae - Continuous Time Paradigms in Logic and Automata
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We develop a unified functional formalism for modelling complex systems, that is to say systems that are composed of a number of heterogeneous components, including typically software and physical devices. Our approach relies on non-standard analysis that allows us to model continuous time in a discrete way. S ystems are defined as generalized Turing machines with temporized input, internal and output mechanisms. Behaviors of systems are represented by transfer functions. A transfer function is said to be implementable if it is associated with a system. This notion leads us to define a new class - which is natural in our framework - of computable functions on (usual) real numbers. We show that our definitions are robust: on one hand, the class of implementable transfer functions is closed under composition; on the other hand, the class of computable functions in our meaning includes analytical functions whose coefficients are computable in the usual way, and is closed under addition, multiplication, differentiation and integration. Our class of computable functions also includes solutions of dynamical and Hamiltonian systems defined by computable functions. Hence, our notion of system appears to take suitably into account physical systems.