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Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…
We give several different encodings of the step function of a Turing machine in intuitionistic linear logic, and calculate the denotations of these encodings in the Sweedler semantics.
Effective control and prediction of dynamical systems often require appropriate handling of continuous-time and discrete, event-triggered processes. Stochastic hybrid systems (SHSs), common across engineering domains, provide a formalism…
The SPaCIFY project, which aims at bringing advances in MDE to the satellite flight software industry, advocates a top-down approach built on a domain-specific modeling language named Synoptic. In line with previous approaches to real-time…
Decomposing the domain of a function into parts has many uses in mathematics. A domain may naturally be a union of pieces, a function may be defined by cases, or different boundary conditions may hold on different regions. For any…
This paper is a survey of extensions to finite automata theory to model real-time systems as well as systems exhibiting mixed discrete-continuous behavior. Real-time systems maintain a continuous and timely interaction with the environment,…
Humans achieve complex manipulation through coordinated whole-body control, whereas most Vision-Language-Action (VLA) models treat robot body parts largely independently, making high-DoF humanoid control challenging and often unstable. We…
Performing multiple computations within the same system, without spatial or temporal separation of tasks, requires encoding multiple data items into a well-defined physical state. The most widely explored mechanism for such encoding is the…
Probabilistic and stochastic behavior are omnipresent in computer controlled systems, in particular, so-called safety-critical hybrid systems, because of fundamental properties of nature, uncertain environments, or simplifications to…
We propose the Manifold Function Encoder (MFE) for identifying different functions defined on different manifolds. Both a manifold in Euclidean space and a function defined on this manifold can be viewed as bounded linear functionals on a…
We use dense variable-ordering to define HRD (Hybrid-Restriction Diagram), a new BDD-like data-structure for the representation and manipulation of state-spaces of linear hybrid automata. We present and discuss various manipulation…
Advanced embedded algorithms are growing in complexity and they are an essential contributor to the growth of autonomy in many areas. However, the promise held by these algorithms cannot be kept without proper attention to the considerably…
The role of the descriptor system representation as basis for reliable numerical computations for system analysis and synthesis, and in particular, for the manipulation of rational matrices, is discussed and available robust numerical…
Via a non degenerate symmetric bilinear form we identify the coadjoint representation with a new representation and so we induce on the orbits a simplectic form. By considering Hamiltonian systems on the orbits we study some features of…
Algorithms are presented for the tanh- and sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions of ODEs and…
The standard engineering approach to modelling of complex systems is highly compositional. In order to be able to understand (or to control) the behavior of a complex dynamical systems, it is often desirable, if not necessary, to view this…
Hybrid systems are dynamical systems with continuous evolution of states and discrete evolution of states and governing equations. We have worked on the design and implementation of HydLa, a constraint-based modeling language for hybrid…
Bialgebras and Hopf (bi)modules are typical algebraic structures with several interacting operations. Their structural and homological study is therefore quite involved. We develop the machinery of braided systems, tailored for handling…
Solving symbolic reasoning problems that require compositionality and systematicity is considered one of the key ingredients of human intelligence. However, symbolic reasoning is still a great challenge for deep learning models, which often…
This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. The proposed procedure has several features which distinguishes it from the other procedures for the problem. First of all a sliding…