7 research outputs found
How to kill epsilons with a dagger: a coalgebraic take on systems with algebraic label structure
We propose an abstract framework for modeling state-based systems with internal behavior as e.g. given by silent or ϵ-transitions. Our approach employs monads with a parametrized fixpoint operator †to give a semantics to those systems and implement a sound procedure of abstraction of the internal transitions, whose labels are seen as the unit of a free monoid. More broadly, our approach extends the standard coalgebraic framework for state-based systems by taking into account the algebraic structure of the labels of their transitions. This allows to consider a wide range of other examples, including Mazurkiewicz traces for concurrent systems.Funded by the ERDF through the Programme COMPETE and by the Portuguese Foundation for Science and Technology, project ref. FCOMP-01-0124-FEDER-020537 and SFRH/BPD/71956/2010. Acknowledge support by project ANR 12IS0 2001 PACE
Fair Simulation for Nondeterministic and Probabilistic Buechi Automata: a Coalgebraic Perspective
Notions of simulation, among other uses, provide a computationally tractable
and sound (but not necessarily complete) proof method for language inclusion.
They have been comprehensively studied by Lynch and Vaandrager for
nondeterministic and timed systems; for B\"{u}chi automata the notion of fair
simulation has been introduced by Henzinger, Kupferman and Rajamani. We
contribute to a generalization of fair simulation in two different directions:
one for nondeterministic tree automata previously studied by Bomhard; and the
other for probabilistic word automata with finite state spaces, both under the
B\"{u}chi acceptance condition. The former nondeterministic definition is
formulated in terms of systems of fixed-point equations, hence is readily
translated to parity games and is then amenable to Jurdzi\'{n}ski's algorithm;
the latter probabilistic definition bears a strong ranking-function flavor.
These two different-looking definitions are derived from one source, namely our
coalgebraic modeling of B\"{u}chi automata. Based on these coalgebraic
observations, we also prove their soundness: a simulation indeed witnesses
language inclusion
Bialgebraic Semantics for Logic Programming
Bialgebrae provide an abstract framework encompassing the semantics of
different kinds of computational models. In this paper we propose a bialgebraic
approach to the semantics of logic programming. Our methodology is to study
logic programs as reactive systems and exploit abstract techniques developed in
that setting. First we use saturation to model the operational semantics of
logic programs as coalgebrae on presheaves. Then, we make explicit the
underlying algebraic structure by using bialgebrae on presheaves. The resulting
semantics turns out to be compositional with respect to conjunction and term
substitution. Also, it encodes a parallel model of computation, whose soundness
is guaranteed by a built-in notion of synchronisation between different
threads
Interacting Hopf Algebras: the theory of linear systems
Scientists in diverse fields use diagrammatic formalisms to reason about various kinds
of networks, or compound systems. Examples include electrical circuits, signal flow graphs,
Penrose and Feynman diagrams, Bayesian networks, Petri nets, Kahn process networks, proof
nets, UML specifications, amongst many others. Graphical languages provide a convenient
abstraction of some underlying mathematical formalism, which gives meaning to diagrams.
For instance, signal flow graphs, foundational structures in control theory, are traditionally
translated into systems of linear equations. This is typical: diagrammatic languages are used
as an interface for more traditional mathematics, but rarely studied per se.
Recent trends in computer science analyse diagrams as first-class objects using formal
methods from programming language semantics. In many such approaches, diagrams are generated
as the arrows of a PROP — a special kind of monoidal category — by a two-dimensional
syntax and equations. The domain of interpretation of diagrams is also formalised as a PROP
and the (compositional) semantics is expressed as a functor preserving the PROP structure.
The first main contribution of this thesis is the characterisation of SVk, the PROP of
linear subspaces over a field k. This is an important domain of interpretation for diagrams
appearing in diverse research areas, like the signal flow graphs mentioned above. We present by
generators and equations the PROP IH of string diagrams whose free model is SVk. The name
IH stands for interacting Hopf algebras: indeed, the equations of IH arise by distributive laws
between Hopf algebras, which we obtain using Lack’s technique for composing PROPs. The
significance of the result is two-fold. On the one hand, it offers a canonical string diagrammatic
syntax for linear algebra: linear maps, kernels, subspaces and the standard linear algebraic
transformations are all faithfully represented in the graphical language. On the other hand,
the equations of IH describe familiar algebraic structures — Hopf algebras and Frobenius
algebras — which are at the heart of graphical formalisms as seemingly diverse as quantum
circuits, signal flow graphs, simple electrical circuits and Petri nets. Our characterisation
enlightens the provenance of these axioms and reveals their linear algebraic nature.
Our second main contribution is an application of IH to the semantics of signal processing
circuits. We develop a formal theory of signal flow graphs, featuring a string diagrammatic
syntax for circuits, a structural operational semantics and a denotational semantics. We
prove soundness and completeness of the equations of IH for denotational equivalence. Also,
we study the full abstraction question: it turns out that the purely operational picture is
too concrete — two graphs that are denotationally equal may exhibit different operational
behaviour. We classify the ways in which this can occur and show that any graph can be
realised — rewritten, using the equations of IH, into an executable form where the operational
behaviour and the denotation coincide. This realisability theorem — which is the culmination
of our developments — suggests a reflection about the role of causality in the semantics of
signal flow graphs and, more generally, of computing devices
PolÃticas de Copyright de Publicações CientÃficas em Repositórios Institucionais: O Caso do INESC TEC
A progressiva transformação das práticas cientÃficas, impulsionada pelo desenvolvimento das novas Tecnologias de Informação e Comunicação (TIC), têm possibilitado aumentar o acesso à informação, caminhando gradualmente para uma abertura do ciclo de pesquisa. Isto permitirá resolver a longo prazo uma adversidade que se tem colocado aos investigadores, que passa pela existência de barreiras que limitam as condições de acesso, sejam estas geográficas ou financeiras. Apesar da produção cientÃfica ser dominada, maioritariamente, por grandes editoras comerciais, estando sujeita à s regras por estas impostas, o Movimento do Acesso Aberto cuja primeira declaração pública, a Declaração de Budapeste (BOAI), é de 2002, vem propor alterações significativas que beneficiam os autores e os leitores. Este Movimento vem a ganhar importância em Portugal desde 2003, com a constituição do primeiro repositório institucional a nÃvel nacional. Os repositórios institucionais surgiram como uma ferramenta de divulgação da produção cientÃfica de uma instituição, com o intuito de permitir abrir aos resultados da investigação, quer antes da publicação e do próprio processo de arbitragem (preprint), quer depois (postprint), e, consequentemente, aumentar a visibilidade do trabalho desenvolvido por um investigador e a respetiva instituição. O estudo apresentado, que passou por uma análise das polÃticas de copyright das publicações cientÃficas mais relevantes do INESC TEC, permitiu não só perceber que as editoras adotam cada vez mais polÃticas que possibilitam o auto-arquivo das publicações em repositórios institucionais, como também que existe todo um trabalho de sensibilização a percorrer, não só para os investigadores, como para a instituição e toda a sociedade. A produção de um conjunto de recomendações, que passam pela implementação de uma polÃtica institucional que incentive o auto-arquivo das publicações desenvolvidas no âmbito institucional no repositório, serve como mote para uma maior valorização da produção cientÃfica do INESC TEC.The progressive transformation of scientific practices, driven by the development of new Information and Communication Technologies (ICT), which made it possible to increase access to information, gradually moving towards an opening of the research cycle. This opening makes it possible to resolve, in the long term, the adversity that has been placed on researchers, which involves the existence of barriers that limit access conditions, whether geographical or financial. Although large commercial publishers predominantly dominate scientific production and subject it to the rules imposed by them, the Open Access movement whose first public declaration, the Budapest Declaration (BOAI), was in 2002, proposes significant changes that benefit the authors and the readers. This Movement has gained importance in Portugal since 2003, with the constitution of the first institutional repository at the national level. Institutional repositories have emerged as a tool for disseminating the scientific production of an institution to open the results of the research, both before publication and the preprint process and postprint, increase the visibility of work done by an investigator and his or her institution. The present study, which underwent an analysis of the copyright policies of INESC TEC most relevant scientific publications, allowed not only to realize that publishers are increasingly adopting policies that make it possible to self-archive publications in institutional repositories, all the work of raising awareness, not only for researchers but also for the institution and the whole society. The production of a set of recommendations, which go through the implementation of an institutional policy that encourages the self-archiving of the publications developed in the institutional scope in the repository, serves as a motto for a greater appreciation of the scientific production of INESC TEC