Related papers: An Algebraic Treatment of Recursion
A central method for analyzing the asymptotic complexity of a functional program is to extract and then solve a recurrence that expresses evaluation cost in terms of input size. The relevant notion of input size is often specific to a…
We use Hidden Markov Models to motivate a quantitative compositional semantics for noninterference-based security with iteration, including a refinement- or "implements" relation that compares two programs with respect to their information…
Boolean grammars generalize context-free rewriting by extending the possibilities when dealing with different rules for the same nonterminal symbol. By allowing not only disjunction (as in the case of usual context-free grammars), but also…
We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…
We present a process algebra aimed at describing interactions that are multiparty, i.e. that may involve more than two processes and that are open, i.e. the number of the processes they involve is not fixed or known a priori. Here we focus…
The analysis of solutions to algebraic equations is further simplified. A couple of functions and their analytic continuation or root findings are required.
It is well known that general recursion cannot be expressed within Martin-Loef's type theory and various approaches have been proposed to overcome this problem still maintaining the termination of the computation of the typable terms. In…
This survey provides an elementary introduction to operads and to their applications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the necessity to have an algebraic object which encodes higher…
We introduce and characterize a particularly tractable class of unital type 1 C*-algebras with bounded dimension of irreducible representations. Algebras in this class are called recursive subhomogeneous algebras, and they have an inductive…
Linear algebra is usually defined over a field such as the reals or complex numbers. It is possible to extend this to skew fields such as the quaternions. However, to the authors' knowledge there is no commonly accepted notation of linear…
In software engineering, taking a good election between recursion and iteration is essential because their efficiency and maintenance are different. In fact, developers often need to transform iteration into recursion (e.g., in debugging,…
We present a computer-supported approach for the logical analysis and conceptual explicitation of argumentative discourse. Computational hermeneutics harnesses recent progresses in automated reasoning for higher-order logics and aims at…
In this paper we generalize notions of iterated integral with regard to an unpredictable process. We establish a formula of integration by parts, the existence of a continuous modification and give an expression of the increasing process.
Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove logarithmic…
Models of iterated computation, such as (completely) iterative monads, often depend on a notion of guardedness, which guarantees unique solvability of recursive equations and requires roughly that recursive calls happen only under certain…
In this paper, we present a partial survey of the tools borrowed from tensor algebra, which have been utilized recently in Statistics and Signal Processing. It is shown why the decompositions well known in linear algebra can hardly be…
Using standard domain-theoretic fixed-points, we present an approach for defining recursive functions that are formulated in monadic style. The method works both in the simple option monad and the state-exception monad of Isabelle/HOL's…
The computation of matrix functions is a well-studied problem. Of special importance are the exponential and the logarithm of a matrix, where the latter also raises existence and uniqueness questions. This is particularly relevant in the…
This is a list of some problems and conjectures related to various types of algebras, that is to algebraic operads. Some comments and hints are included.
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…