Related papers: An Algebraic Treatment of Recursion
Higher-order tensors appear in various areas of mechanics as well as physics, medicine or earth sciences. As these tensors are highly complex, most are not well understood. Thus, the analysis and the visualization process form a highly…
In arXiv:2204.03190, we proposed a universal method to reduce one-loop integrals with both tensor structure and higher-power propagators. But the method is quite redundant as it does not utilize the results of lower rank cases when…
Abductive forgetting is removing variables from a logical formula while maintaining its abductive explanations. It is carried in two alternative ways depending on its intended application. Both differ from the usual forgetting, which…
Often, we assume that an action is permitted simply because it is not explicitly forbidden; or, similarly, that an action is forbidden simply because it is not explicitly permitted. This kind of assumptions appear, e.g., in autonomous…
We take a categorical approach to describe ternary derivations and ternary automorphisms of triangular algebras. New classes of automorphisms and derivations of triangular algebras are also introduced and studied.
A process algebra is proposed, whose semantics maps a term to a nondeterministic finite automaton (NFA, for short). We prove a representability theorem: for each NFA $N$, there exists a process algebraic term $p$ such that its semantics is…
The object of the present paper is to extend the third-order iterative method for solving nonlinear equations into systems of nonlinear equations. Since our motive is to develop the method which improve the order of convergence of Newton's…
Process algebra ACP based on the interleaving semantics can not be reversed. We design a reversible version of APTC called RAPTC. It has algebraic laws of reversible choice, sequence, parallelism, communication, silent step and abstraction,…
A standard informal method for analyzing the asymptotic complexity of a program is to extract a recurrence that describes its cost in terms of the size of its input, and then to compute a closed-form upper bound on that recurrence. We give…
This paper presents the equality of finite index sums of Bessel func- tions containing arbitrary numbers of terms. These reduce to the familiar three term recursion formulas in simple cases.
Finding a denotational semantics for higher order quantum computation is a long-standing problem in the semantics of quantum programming languages. Most past approaches to this problem fell short in one way or another, either limiting the…
We present a process algebra based approach to formalize the interactions of computing devices such as the representation of policies and the resolution of conflicts. As an example we specify how promises may be used in coming to an…
Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…
The concept of decomposition in computer science and engineering is considered a fundamental component of computational thinking and is prevalent in design of algorithms, software construction, hardware design, and more. We propose a simple…
Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that…
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected…
We carry out a proof theoretic analysis of the wellfoundedness of recursive path orders in an abstract setting. We outline a very general termination principle and extract from its wellfoundedness proof subrecursive bounds on the size of…
Digital circuits, despite having been studied for nearly a century and used at scale for about half that time, have until recently evaded a fully compositional theoretical in which arbitrary circuits may be freely composed together without…
We derive recursions for the probability distribution of random sums by computer algebra. Unlike the well-known Panjer-type recursions, they are of finite order and thus allow for computation in linear time. This efficiency is bought by the…
We present Russell's antinomy using three distinct deductive systems, which are then compared to deepen the logical deductions that lead to the contradiction. Some inferential paths are then presented, alternative to the commonly accepted…