We introduce and study the model of simply generated non-crossing partitions, which are, roughly speaking, chosen at random according to a sequence of weights. This framework encompasses the particular case of uniform non-crossing partitions with constraints on their block sizes. Our main tool is a bijection between non-crossing partitions and plane trees, which maps such simply generated non-c...

UML is a standard language for specifying, visualizing, constructing, and documenting the artifacts of software systems. UML was created by Object Management Group (OMG) and UML 1.0 specification draft was proposed to the OMG in January 1997. OMG is continuously putting effort to make a truly industry standard.  UML stands for Unified Modelling Language.  UML is different from the other commo...

A finite group G is said to be simply reducible (SR-group) if it has the following two properties: 1) each element of G is conjugate to its inverse; 2) the tensor product of every two irreducible representations is decomposed as a sum of irreducible representations of G with multiplicities not exceeding 1. It is proved that a finite SR-group is solvable if it has no composition factors isomorph...

The termination method of weakly monotonic algebras, which has been defined for higher-order rewriting in the HRS formalism, offers a lot of power, but has seen little use in recent years. We adapt and extend this method to the alternative formalism of algebraic functional systems, where the simply-typed λ-calculus is combined with algebraic reduction. Using this theory, we define higher-order ...

This study explores the scope properties of some indefinites in Japanese in terms of epsilon calculus. Different from ordinary noun phrases, quantificational noun phrases like indefinites are assigned higher-order categories and/or types in syntax, and taken to denote functions from sets to truth values in semantics, which results in great difficulty in deriving proper interpretations of senten...

In the pursuit of enhanced competitiveness organisations are today searching for innovative business models in order to foster economic benefits. In Slovenia, several clusters are being formed, including the Slovenian Transport Logistics Cluster (STLC) as one of the most important. The STLC is currently in the stage of dynamic growth, demanding business model formation and adequate informatisat...

We consider the following question: in the simply-typed λ-calculus with algebraic operations, is the set of equations valid in a particular model exactly those provable from (β), (η), and the set of algebraic equations, E, that are valid in the model? We find conditions for determining whether βηE-equational reasoning is complete. We demonstrate the utility of the results by presenting a number...

We define a notion of recognizable sets of simply typed λterms that extends the notion of recognizable sets of strings or trees. This definition is based on finite models. Using intersection types, we generalize the notions of automata for strings and trees so as to grasp recognizability for λ-terms. We then expose the closure properties of this notion and present some of its applications.