We present a formal derivation of program schemes that are usually called Backtracking programs and Branch-and-Bound programs. The derivation consists of a series of transformation steps, specifically algebraic manipulations, on the initial specification until the desired programs are obtained. The well-known notions of linear recursion and tail recursion are extended, for structures, to elemen...

Recursion is a fundamental concept in computer science. Creating a correct mental model for the concept of recursion allows the understanding of recursive algorithms and their correct implementation. Teaching recursion is not an easy task for teachers. Generally, supporting abstract concepts through graphics leads to a better understanding of them. This paper presents a graphical application th...

Abstract. In this paper we study effective recursion formulae for computing intersection numbers of mixed ψ and κ classes on moduli spaces of curves. By using the celebrated WittenKontsevich theorem, we generalize Mulase-Safnuk form of Mirzakhani’s recursion and prove a recursion formula of higher Weil-Petersson volumes. We also present recursion formulae to compute intersection pairings in the...

Harer and Zagier proved a recursion to enumerate gluings of 2d-gon that result in an orientable genus g surface, their work on Euler characteristics moduli spaces curves. Analogous results have been discovered for other enumerative problems, so it is natural pose the following question: how large family problems which these so-called 1-point recursions exist? In this paper, we prove existence c...

Dynamic programming is an algorithm design technique, which allows to improve efficiency by avoiding re-computation of identical subtasks. We present a new recursion combinator, dynamorphism, which captures the dynamic programming recursion pattern with memoization and identify some simple conditions when functions defined by structured general recursion can be redefined as a dynamorphism. The ...

We present a two-parameter family of recursion formulas for scalar field theory. The first parameter is the dimension (D). The second parameter (ζ) allows one to continuously extrapolate between Wilson’s approximate recursion formula and the recursion formula of Dyson’s hierarchical model. We show numerically that at fixed D, the critical exponent γ depends continuously on ζ. We suggest the use...

Abstract In this paper, we construct the cut‐and‐join operator description for generating functions of all intersection numbers , and classes on moduli spaces . The operators define an algebraic version topological recursion. This recursion allows us to compute these recursively. For specific values parameters, describe volumes (super) hyperbolic Riemann surfaces with geodesic boundaries, which...

Recursion-free Constrained Horn Clauses (CHCs) are logicprogramming problems that formulate verifying safety of programs with bounded iteration and recursion. They both formulate bounded verification problems and are generated by solvers that attempt to verify safety of unbounded iterative or recursive systems. Efficient solvers of recursion-free systems reduce the problem to solving a series o...

Several problems in recursion theory on admissible o¡dinals (a -recursion theory) and recursion theory on inadmissible ordinals (B -recursion theory) are studied. Fruitful interactions betweenboth theories are stressed. In the fr¡stpart the admissible collapse is used in order to characterizefor some inadmissible B the structure of all p -recursively enumerable degrees asanaccumulationof struct...