Related papers: Enumeration of generalized $BCI$ lambda-terms

We define the concept of a logic frame, which extends the concept of an abstract logic by adding the concept of a syntax and an axiom system. In a recursive logic frame the syntax and the set of axioms are recursively coded. A recursive…

Let $c_n$ denote the number of nodes at a distance $n$ from the root of a rooted tree. A criterion for proving the rationality and computing the rational generating function of the sequence $\{c_n\}$ is described. This criterion is applied…

We propose a call-by-value lambda calculus extended with a new construct inspired by abductive inference and motivated by the programming idioms of machine learning. Although syntactically simple the abductive construct has a complex and…

A prototypical example of categorial grammars are those based on Lambek calculus, i.e. noncommutative intuitionistic linear logic. However, it has been noted that purely noncommutative operations are often not sufficient for modeling even…

For an arbitrary homogeneous linear recurrence sequence of order d with constant coefficients, we derive recurrence relations for all subsequences with indices in arithmetic progression. The coefficients of these recurrences are given…

We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…

Let (F_n^{(k)})_{n\geq -(k-2)} be the k-generalized Fibonacci sequence, defined as the linear recurrence sequence whose first k terms are \(0, 0, \ldots, 0, 1\), and whose subsequent terms are determined by the sum of the preceding k terms.…

In a previous paper an asymptotic expansion for lambda_d in powers of 1/d was developed. The results of computer computations for some terms in the expansion, as well as various quantities associated to the expansion, are herein presented.…

In this work, we study general Dirichlet coalescents, which are a family of Xi-coalecents constructed from i.i.d mass partitions, and are an extension of the symmetric coalescent. This class of models is motivated by population models with…

Let $I(b,d,k)$ be the subseries of the harmonic series keeping the integers having exactly $k$ occurrences of the digit $d$ in base $b$. We prove the existence of an asymptotic expansion to all orders in descending powers of $b$, for fixed…

The theory of asymptotic complexity provides an approach to characterizing the behavior of programs in terms of bounds on the number of computational steps executed or use of computational resources. We describe work using ACL2 to prove…

This article presents a combinatorial result on indexed languages which was inspired by an attempt to understand the structure of groups with indexed language word problem. We show that a sufficiently long word in an indexed language can be…

In a recent paper (Tran et al., Ann.Phys.311(2004)204), some asymptotic number theoretical results on the partitioning of an integer were derived exploiting its connection to the quantum density of states of a many-particle system. We…

This survey article is devoted to general results in combinatorial enumeration. The first part surveys results on growth of hereditary properties of combinatorial structures. These include permutations, ordered and unordered graphs and…

We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…

A typical way of analyzing the time complexity of functional programs is to extract a recurrence expressing the running time of the program in terms of the size of its input, and then to solve the recurrence to obtain a big-O bound. For…

A common theme of enumerative combinatorics is formed by counting functions that are polynomials evaluated at positive integers. In this expository paper, we focus on four families of such counting functions connected to hyperplane…

In the lambda calculus a term is solvable iff it is operationally relevant. Solvable terms are a superset of the terms that convert to a final result called normal form. Unsolvable terms are operationally irrelevant and can be equated…

We investigate the interplay between a modality for controlling the behaviour of recursive functional programs on infinite structures which are completely silent in the syntax. The latter means that programs do not contain "marks" showing…

We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the…