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We develop a compositional approach for automatic and symbolic differentiation based on categorical constructions in functional analysis where derivatives are linear functions on abstract vectors rather than being limited to scalars,…
In [1], an operator was introduced which acts parallel to the Riemann-Liouville differintegral on a transformation of the space of real analytic functions and commutes with itself. This paper aims to extend the technique - and its defining…
In this paper, we develop a compositional scheme for the construction of continuous approximations for interconnections of infinitely many discrete-time switched systems. An approximation (also known as abstraction) is itself a…
Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…
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…
We provide a proof for one version of Pisot conjecture. We make use of the weak mixing property of the subshift of finite type derived from the prefix-suffix automaton to conclude that the substitution dynamical system has pure discrete…
Functional decomposition is the process of breaking down a function $f$ into a composition $f=g(f_1,\dots,f_k)$ of simpler functions $f_1,\dots,f_k$ belonging to some class $\mathcal{F}$. This fundamental notion can be used to model…
The article is devoted to one infinite parametric class of continuous functions with complicated local structure. In the article differential, integral, self-affine and other properties of functions, that their argument is represented by…
While automata theory often concerns itself with regular predicates, relations corresponding to acceptance by a finite state automaton, in this article we study the regular functions, such relations which are also functions in the…
Commutativity of program code (i.e. the equivalence of two code fragments composed in alternate orders) is of ongoing interest in many settings such as program verification, scalable concurrency, and security analysis. While some have…
We explore denotational interpreters: denotational semantics that produce coinductive traces of a corresponding small-step operational semantics. By parameterising our denotational interpreter over the semantic domain and then varying it,…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
We present a recursive formulation of the Horn algorithm for deciding the satisfiability of propositional clauses. The usual presentations in imperative pseudo-code are informal and not suitable for simple proofs of its main properties. By…
Computational mechanics, an approach to structural complexity, defines a process's causal states and gives a procedure for finding them. We show that the causal-state representation--an $\epsilon$-machine--is the minimal one consistent with…
The functional correspondence is a manual derivation technique transforming higher-order evaluators into the semantically equivalent abstract machines. The transformation consists of two well-known program transformations: translation to…
We completely describe a new domain for abstract interpretation of numerical programs. Fixpoint iteration in this domain is proved to converge to finite precise invariants for (at least) the class of stable linear recursive filters of any…
The Functional Machine Calculus (Heijltjes 2022) is a new approach to unifying the imperative and functional programming paradigms. It extends the lambda-calculus, preserving the key features of confluent reduction and typed termination, to…
Discrete abstractions have become a standard approach to assist control synthesis under complex specifications. Most techniques for the construction of discrete abstractions are based on sampling of both the state and time spaces, which may…
This paper deals with the controllability for a class of non-autonomous neutral differential equations of fractional order with infinite delay in an abstract space. The semi-group theory of bounded linear operators, fractional calculus, and…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and quantum circuits are naturally interpretable in such structures. We…