Isomorphism test for digraphs with weighted edges

Colour refinement is at the heart of all the most efficient graph isomorphism software packages. In this paper we present a method for extending the applicability of refinement algorithms to directed graphs with weighted edges. We use Traces as a reference software, but the proposed solution is easily transferrable to any other refinement-based graph isomorphism tool in the literature. We substantiate the claim that the performances of the original algorithm remain substantially unchanged by showing experiments for some classes of benchmark graphs

Conflict vs causality in event structures

Event structures are one of the best known models for concurrency. Many variants of the basic model and many possible notions of equivalence for them have been devised in the literature. In this paper, we study how the spectrum of equivalences for Labelled Prime Event Structures built by Van Glabbeek and Goltz changes if we consider two simplified notions of event structures: the first is obtained by removing the causality relation (Coherence Spaces) and the second by removing the conflict relation (Elementary Event Structures). As expected, in both cases the spectrum turns out to be simplified, since some notions of equivalence coincide in the simplified settings; actually, we prove that removing causality simplifies the spectrum considerably more than removing conflict. Furthermore, while the labeling of events and their cardinality play no role when removing causality, both the labeling function and the cardinality of the event set dramatically influence the spectrum of equivalences in the conflict-free setting

A System F accounting for scalars

The Algebraic lambda-calculus and the Linear-Algebraic lambda-calculus extend the lambda-calculus with the possibility of making arbitrary linear combinations of terms. In this paper we provide a fine-grained, System F-like type system for the linear-algebraic lambda-calculus. We show that this "scalar" type system enjoys both the subject-reduction property and the strong-normalisation property, our main technical results. The latter yields a significant simplification of the linear-algebraic lambda-calculus itself, by removing the need for some restrictions in its reduction rules. But the more important, original feature of this scalar type system is that it keeps track of 'the amount of a type' that is present in each term. As an example of its use, we shown that it can serve as a guarantee that the normal form of a term is barycentric, i.e that its scalars are summing to one

An Algebraic View of the Böhm-out Technique

AbstractUsing an algebraic representation of closed β-normal forms in λ-calculus, the Böhm's theorem is rephrased as an equality predicate between elements of a term algebra. The presented algebraic interpretation gives new insight into the Böhm-out technique and allows for original applications of the method

Abstraction problems in Combinatory Logic: a compositive approach

AbstractThe problem of the translation of λ-terms into combinators (bracket abstraction) is of great importance for the implementation of functional languages. In the literature there exist a lot of algorithms concerning this topic, each of which is based on a particular choice of a combinatory basis, its cardinality, and an abstraction technique. The algorithm presented here originated from a modification of the definition of abstraction given by Curry in 1930, and has the following interesting properties: 1.(i) it employs a potentially infinite basis of combinators, each of which depends on at most two parameters and is, therefore, directly implementable;2.(ii) it gives compact code, introducing a number of basic combinators which is proportional to the size of the expression to be abstracted and invariant for one- and multi-sweep abstraction techniques;3.(iii) it gives the result in the form RIM1… Mn, where R is a regular combinator expressed as a composition of basic combinators, I is the identity combinator, and M1,…, Mn are the constant terms appearing into the expression subjected to the translation process.It appears that a slight modification of the algorithm yields a combinatory equivalent of Hughes' supercombinators

Il gioco del filetto a tre pedine

Sansoni Editor

Normalization and Extensionality

Computer Society of the IEE