Functorial Semantics for Petri Nets under the Individual Token Philosophy

Although the algebraic semantics of place/transition Petri nets under the collective token philosophy has been fully explained in terms of (strictly) symmetric (strict) monoidal categories, the analogous construction under the individual token philosophy is not completely satisfactory because it lacks universality and also functoriality. We introduce the notion of pre-net to recover these aspects, obtaining a fully satisfactory categorical treatment centered on the notion of adjunction. This allows us to present a purely logical description of net behaviours under the individual token philosophy in terms of theories and theory morphisms in partial membership equational logic, yielding a complete match with the theory developed by the authors for the collective token view of net

Two Algebraic Process Semantics for Contextual Nets

We show that the so-called 'Petri nets are monoids' approach initiated by Meseguer and Montanari can be extended from ordinary place/transition Petri nets to contextual nets by considering suitable non-free monoids of places. The algebraic characterizations of net concurrent computations we provide cover both the collective and the individual token philosophy, uniformly along the two interpretations, and coincide with the classical proposals for place/transition Petri nets in the absence of read-arcs

Diagram techniques for confluence

AbstractWe develop diagram techniques for proving confluence in abstract reductions systems. The underlying theory gives a systematic and uniform framework in which a number of known results, widely scattered throughout the literature, can be understood. These results include Newman's lemma, Lemma 3.1 of Winkler and Buchberger, the Hindley–Rosen lemma, the Request lemmas of Staples, the Strong Confluence lemma of Huet, the lemma of De Bruijn

A Data Transformation System for Biological Data Sources

Scientific data of importance to biologists in the Human Genome Project resides not only in conventional databases, but in structured files maintained in a number of different formats (e.g. ASN.1 and ACE) as well a.s sequence analysis packages (e.g. BLAST and FASTA). These formats and packages contain a number of data types not found in conventional databases, such as lists and variants, and may be deeply nested. We present in this paper techniques for querying and transforming such data, and illustrate their use in a prototype system developed in conjunction with the Human Genome Center for Chromosome 22. We also describe optimizations performed by the system, a crucial issue for bulk data

Kernel P Systems Modelling, Testing and Veri cation

A kernel P system (kP system, for short) integrates in a coherent and elegant manner many of the P system features most successfully used for modelling various applications and, consequently, it provides a framework for analyzing these models. In this paper, we illustrate the modeling capabilities of kernel P systems by showing how other classes of P systems can be represented with this formalism and providing a number of kP system models for sorting algorithms. Furthermore, the problem of testing systems modelled as kP systems is also discussed and a test generation method based on automata is proposed. We also demonstrate how formal veri cation can be used to validate that the given models work as desired

A Linear Category of Polynomial Diagrams

We present a categorical model for intuitionistic linear logic where objects are polynomial diagrams and morphisms are simulation diagrams. The multiplicative structure (tensor product and its adjoint) can be defined in any locally cartesian closed category, whereas the additive (product and coproduct) and exponential Tensor-comonoid comonad) structures require additional properties and are only developed in the category Set, where the objects and morphisms have natural interpretations in terms of games, simulation and strategies.Comment: 20 page

An integration of Euler's pentagonal partition

A recurrent formula is presented, for the enumeration of the compositions of positive integers as sums over multisets of positive integers, that closely resembles Euler's recurrence based on the pentagonal numbers, but where the coefficients result from a discrete integration of Euler's coefficients. Both a bijective proof and one based on generating functions show the equivalence of the subject recurrences.Comment: 22 pages, 2 figures. The recurrence investigated in this paper is essentially that proposed in Exercise 5.2.3 of Igor Pak's "Partition bijections, a survey", Ramanujan J. 12 (2006), but casted in a different form and, perhaps more interestingly, endowed with a bijective proof which arises from a construction by induction on maximal part