Towards Nominal Formal Languages

We introduce formal languages over infinite alphabets where words may contain binders. We define the notions of nominal language, nominal monoid, and nominal regular expressions. Moreover, we extend history-dependent automata (HD-automata) by adding stack, and study the recognisability of nominal languages

Axiomatisation and decidability of multi-dimensional Duration Calculus

AbstractThe Shape Calculus is a spatio-temporal logic based on an n-dimensional Duration Calculus tailored for the specification and verification of mobile real-time systems. After showing non-axiomatisability, we give a complete embedding in n-dimensional interval temporal logic and present two different decidable subsets, which are important for tool support and practical use

Coalgebraic minimization of HD-automata for the π-calculus using polymorphic types

AbstractWe introduce finite-state verification techniques for the π-calculus whose design and correctness are justified coalgebraically. In particular, we formally specify and implement a minimization algorithm for HD-automata derived from π-calculus agents. The algorithm is a generalization of the partition refinement algorithm for classical automata and is specified as a coalgebraic construction defined using λ→,Π,Σ, a polymorphic λ-calculus with dependent types. The convergence of the algorithm is proved; moreover, the correspondence of the specification and the implementation is shown

Families of Symmetries as Efficient Models of Resource Binding

AbstractCalculi that feature resource-allocating constructs (e.g. the pi-calculus or the fusion calculus) require special kinds of models. The best-known ones are presheaves and nominal sets. But named sets have the advantage of being finite in a wide range of cases where the other two are infinite. The three models are equivalent. Finiteness of named sets is strictly related to the notion of finite support in nominal sets and the corresponding presheaves. We show that named sets are generalisd by the categorical model of families, that is, free coproduct completions, indexed by symmetries, and explain how locality of interfaces gives good computational properties to families. We generalise previous equivalence results by introducing a notion of minimal support in presheaf categories indexed over small categories of monos. Functors and categories of coalgebras may be defined over families. We show that the final coalgebra has the greatest possible symmetry up-to bisimilarity, which can be computed by iteration along the terminal sequence, thanks to finiteness of the representation

A Class of Automata for the Verification of Infinite, Resource-Allocating Behaviours

Process calculi for service-oriented computing often feature generation of fresh resources. So-called nominal automata have been studied both as semantic models for such calculi, and as acceptors of languages of finite words over infinite alphabets. In this paper we investi-gate nominal automata that accept infinite words. These automata are a generalisation of deterministic Muller automata to the setting of nominal sets. We prove decidability of complement, union, intersection, emptiness and equivalence, and determinacy by ultimately periodic words. The key to obtain such results is to use finite representations of the (otherwise infinite-state) defined class of automata. The definition of such operations enables model checking of process calculi featuring infinite behaviours, and resource allocation, to be implemented using classical automata-theoretic methods

Using automata to characterise fixed point temporal logics

This work examines propositional fixed point temporal and modal logics called mu-calculi and their relationship to automata on infinite strings and trees. We use correspondences between formulae and automata to explore definability in mu-calculi and their fragments, to provide normal forms for formulae, and to prove completeness of axiomatisations. The study of such methods for describing infinitary languages is of fundamental importance to the areas of computer science dealing with non-terminating computations, in particular to the specification and verification of concurrent and reactive systems. To emphasise the close relationship between formulae of mu-calculi and alternating automata, we introduce a new first recurrence acceptance condition for automata, checking intuitively whether the first infinitely often occurring state in a run is accepting. Alternating first recurrence automata can be identified with mu-calculus formulae, and ordinary, non-alternating first recurrence automata with formulae in a particular normal form, the strongly aconjunctive form. Automata with more traditional Büchi and Rabin acceptance conditions can be easily unwound to first recurrence automata, i.e. to mu-calculus formulae. In the other direction, we describe a powerset operation for automata that corresponds to fixpoints, allowing us to translate formulae inductively to ordinary Büchi and Rabin-automata. These translations give easy proofs of the facts that Rabin-automata, the full mu-calculus, its strongly aconjunctive fragment and the monadic second-order calculus of n successors SnS are all equiexpressive, that Büchi-automata, the fixpoint alternation class Pi_2 and the strongly aconjunctive fragment of Pi_2 are similarly related, and that the weak SnS and the fixpoint-alternation-free fragment of mu-calculus also coincide. As corollaries we obtain Rabin's complementation lemma and the powerful decidability result of SnS. We then describe a direct tableau decision method for modal and linear-time mu-calculi, based on the notion of definition trees. The tableaux can be interpreted as first recurrence automata, so the construction can also be viewed as a transformation to the strongly aconjunctive normal form. Finally, we present solutions to two open axiomatisation problems, for the linear-time mu-calculus and its extension with path quantifiers. Both completeness proofs are based on transforming formulae to normal forms inspired by automata. In extending the completeness result of the linear-time mu-calculus to the version with path quantifiers, the essential problem is capturing the limit closure property of paths in an axiomatisation. To this purpose, we introduce a new \exists\nu-induction inference rule

On SAT representations of XOR constraints

We study the representation of systems S of linear equations over the two-element field (aka xor- or parity-constraints) via conjunctive normal forms F (boolean clause-sets). First we consider the problem of finding an "arc-consistent" representation ("AC"), meaning that unit-clause propagation will fix all forced assignments for all possible instantiations of the xor-variables. Our main negative result is that there is no polysize AC-representation in general. On the positive side we show that finding such an AC-representation is fixed-parameter tractable (fpt) in the number of equations. Then we turn to a stronger criterion of representation, namely propagation completeness ("PC") --- while AC only covers the variables of S, now all the variables in F (the variables in S plus auxiliary variables) are considered for PC. We show that the standard translation actually yields a PC representation for one equation, but fails so for two equations (in fact arbitrarily badly). We show that with a more intelligent translation we can also easily compute a translation to PC for two equations. We conjecture that computing a representation in PC is fpt in the number of equations.Comment: 39 pages; 2nd v. improved handling of acyclic systems, free-standing proof of the transformation from AC-representations to monotone circuits, improved wording and literature review; 3rd v. updated literature, strengthened treatment of monotonisation, improved discussions; 4th v. update of literature, discussions and formulations, more details and examples; conference v. to appear LATA 201

Complex event types for agent-based simulation

This thesis presents a novel formal modelling language, complex event types (CETs), to describe behaviours in agent-based simulations. CETs are able to describe behaviours at any computationally represented level of abstraction. Behaviours can be specified both in terms of the state transition rules of the agent-based model that generate them and in terms of the state transition structures themselves. Based on CETs, novel computational statistical methods are introduced which allow statistical dependencies between behaviours at different levels to be established. Different dependencies formalise different probabilistic causal relations and Complex Systems constructs such as ‘emergence’ and ‘autopoiesis’. Explicit links are also made between the different types of CET inter-dependency and the theoretical assumptions they represent. With the novel computational statistical methods, three categories of model can be validated and discovered: (i) inter-level models, which define probabilistic dependencies between behaviours at different levels; (ii) multi-level models, which define the set of simulations for which an inter-level model holds; (iii) inferred predictive models, which define latent relationships between behaviours at different levels. The CET modelling language and computational statistical methods are then applied to a novel agent-based model of Colonic Cancer to demonstrate their applicability to Complex Systems sciences such as Systems Biology. This proof of principle model provides a framework for further development of a detailed integrative model of the system, which can progressively incorporate biological data from different levels and scales as these become available

Specification and refinement of software connectors

Tese de doutoramento em Informática (área de conhecimento de Fundamentos da Computação)Modern computer based systems are essentially based on the cooperation of distributed, heterogeneous component organized into open software architectures that, moreover, can survive in loosely-coupled environments and be easily adapted to changing application requirements. Such is the case, for example, of applications designed to take advantage of the increased computational power provided by massively parallel systems or of the whole business of Internet-based software development. In order to develop such systems in a systematic way, the focus in development method has switched, along the last decade, from functional to structural issues: both data and processes are encapsulated into software units which are connected into large systems resorting, to a number of techniques intended to support reusability and modifiability. Actually, the complexity and ubiquity achieved by software in present times makes it imperative, more than ever, the availability of both technologies and sound methods to drive its development. Programming ‘in–the–large’, component–based programming and software architecture become popular expressions which embody this sort of concerns and correspond to driving forces in current software engineering. In such a context this thesis aims at introducing formal models for software connectors as well as the corresponding notions of equivalence and refinement upon which calculation principles for reasoning and transforming connector-based software architectures can be developed. This research adopts an exogenous coordination point of view in order to deal with components’ temporal and spatial decoupling and, therefore, to provide support for looser levels of inter-component dependency. The thesis also characterises a notion of behavioural interface for components and services. Interfaces and connectors are put together to form configurations, an abstraction for representing software architectures. A prototype implementation of a subset of the proposed models is provided, in the form of a HASKELL library, as a proof of concept. Furthermore, the thesis reports on a case study in which exogenous coordination is applied to the specification of interactive systems.Um número crescente de sistemas computacionais é baseado na cooperação de componentes interdependentes e heterogêneas, organizadas em arquiteturas abertas capazes de sobreviverem em ambientes altamente distribuídos e facilmente adaptáveis a alterações nos requisitos das aplicações que os suportam. Tal é o caso, por exemplo, de aplicações que exploram o poder computacional de sistemas massivamente paralelos ou de sistemas desenvolvidos sobre a Internet. Para desenvolver este tipo de sistemas de forma sistemática, o foco nos métodos de desenvolvimento alterou-se, ao longo da última década, dos aspectos funcionais para os aspectos estruturais dos sistemas: ambos, estruturas de dados e processos são encapsulados em unidades computacionais que são conectadas em grandes sistemas utilizando-se de diversas técnicas que se pretendem capazes de suportar a reutilização e a adaptabilidade do software. Na realidade, a complexidade e ubiqüidade atingidas pelo software nos dias correntes tornam imperativo, mais do que nunca, a disponibilidade de tecnologias e sólidos métodos para conduzir este processo de desenvolvimento. Programação ’em-grande-escala’, programação baseada em componentes e arquiteturas de software são expressões populares que englobam esta preocupação e correspondem aos esforços direcionados pela engenharia de software. Em tal contexto, esta tese tem por objetivo introduzir modelos formais para conectores de software bem como as correspondentes noções de equivalência e refinamento que suportem cálculos para raciocinar e transformar arquiteturas de software baseada em conectores. Esta pesquisa adota um ponto de vista de coordenação exógena para lidar com a separação espacial e temporal das componentes e suportar níveis elevados de independência entre componentes. A tese caracteriza, ainda, uma noção de interface comportamental para componentes e serviços. Interfaces e conectores agregam-se para formar configurações, uma abstração introduzida para representar arquiteturas de software. A implementação, em protótipo, de parte dos modelos propostos, sob a forma de uma biblioteca em HASKELL, é fornecida como prova de conceito. Finalmente, a tese percorre um estudo de caso em que coordenação exôgena é utilizada na especificação de sistemas interactivos.Fundação para a Ciência e a Tecnologia (FCT), SFRH/BD/11083/200