Search

From 1990 to 2005 the author had the privilege and pleasure to work as a programmer in Farhad Arbab’s research group, initially on the development, implementation and applications of the Manifold coordination language. more...

In this paper, we revise the notion of Soft Constraint Automata, where automata transitions are weighted and consequently each action is associated with a preference value. We first relax the underlying algebraic structure that models preferences, with the purpose to use bipolar preferences (i.e., both positive and negative ones). Then, we equip automata with memory cells, that is, with an internal state to remember and update information from transition to transition. Finally, we revise automata operators, as join and hiding. more...

We discuss an extension of the coordination modeling language Paradigm. The extension is geared towards data-dependent interaction among components, where the coordination is influenced by possibly distributed data. The approach is illustrated by the well-known example of a bakery where tickets are issued to serve clients in order. Also, it is described how to encode Paradigm models with data in the process language of the mCRL2 toolset for further analysis of the coordination. more...

In 1974 Dijkstra introduced the seminal concept of self-stabilization that turned out to be one of the main approaches to fault-tolerant computing. We show here how his three solutions can be formalized and reasoned about using the concepts of game theory. We also determine the precise number of steps needed to reach self-stabilization in his first solution. more...

Streams, or infinite sequences, are infinite objects of a very simple type, yet they have a rich theory partly due to their ubiquity in mathematics and computer science. Stream differential equations are a coinductive method for specifying streams and stream operations, and their theory has been developed in many papers over the past two decades. In this paper we present a survey of the many results in this area. Our focus is on the classification of different formats of stream differential equations, their solution methods, and the classes of streams they can define. Moreover, we describe in detail the connection between the so-called syntactic solution method and abstract GSOS. more...

Initial Semantics aims at interpreting the syntax associated to a signature as the initial object of some category of 'models', yielding induction and recursion principles for abstract syntax. Zsid\'o proves an initiality result for simply-typed syntax: given a signature S, the abstract syntax associated to S constitutes the initial object in a category of models of S in monads. However, the iteration principle her theorem provides only accounts for translations between two languages over a fixed set of object types. We generalize Zsid\'o's notion of model such that object types may vary, yielding a larger category, while preserving initiality of the syntax therein. Thus we obtain an extended initiality theorem for typed abstract syntax, in which translations between terms over different types can be specified via the associated category-theoretic iteration operator as an initial morphism. Our definitions ensure that translations specified via initiality are type-safe, i.e. compatible with the typing in the source and target language in the obvious sense. Our main example is given via the propositions-as-types paradigm: we specify propositions and inference rules of classical and intuitionistic propositional logics through their respective typed signatures. Afterwards we use the category--theoretic iteration operator to specify a double negation translation from the former to the latter. A second example is given by the signature of PCF. For this particular case, we formalize the theorem in the proof assistant Coq. Afterwards we specify, via the category-theoretic iteration operator, translations from PCF to the untyped lambda calculus. more...

Coalgebra is an abstract framework for the uniform study of different kinds of dynamical systems. An endofunctor $F$ determines both the type of systems ($F$-coalgebras) and a notion of behavioral equivalence ($\sim_F$) amongst them. Many types of transition systems and their equivalences can be captured by a functor $F$. For example, for deterministic automata the derived equivalence is language equivalence, while for non-deterministic automata it is ordinary bisimilarity. The powerset construction is a standard method for converting a nondeterministic automaton into an equivalent deterministic one as far as language is concerned. In this paper, we lift the powerset construction on automata to the more general framework of coalgebras with structured state spaces. Examples of applications include partial Mealy machines, (structured) Moore automata, and Rabin probabilistic automata. more...

We show that coinductive predicates expressing behavioural properties of infinite objects can be themselves expressed as final coalgebras in a category of relations. The well-known case of bisimulation will simply be a special case of such final predicates. We will show how some useful pointwise and mixed properties of streams can be modelled in this way. more...