Nordic Workshop Programming Theory 

Abstract: We axiomatize the congruence relation for binding bigraphs and prove that the generated theory is complete. In doing so, we define a normal form for binding bigraphs, and prove that it is unique up to certain isomorphisms.Our work builds on Milner's axioms for pure bigraphs. We have extended the set of axioms with five new axioms concerned with binding, and we have altered some of Milner's axioms for ions, because ions in binding bigraphs have names on both their inner and outer faces. The resulting theory is a conservative extension of Milner's for pure bigraphs.

Abstract: We present a novel canonical automaton model, based on register automata, that can be used to specify protocol or program behavior. Register automata have a finite control structure and a finite number of registers (variables), and process sequences of terms that carry data values from an infinite domain. We consider register automata that compare data values for equality. A major contribution is the definition of a canonical automaton representation of any language recognizable by a deterministic register automaton, by means of a Nerode congruence. This canonical form is well suited for modeling, e.g., protocols or program behavior. Our model can be exponentially more succinct than previous proposals, since it filters out ‘accidental’ relations between data values. This opens the way to new practical applications, e.g., in automata learning.

Abstract: The channel capacity of a deterministic system with confidential data is an upper bound on the amount of bits of data an attacker can learn from the system. We encode all possible attacks to a system using a probabilistic specification, an Interval Markov Chain. Then the channel capacity computation reduces to finding a model of a specification with highest entropy. Entropy maximization for probabilistic process specifications has not been studied before, even though it is well known in Bayesian inference for discrete distributions. We give a characterization of global entropy of a process as a reward function, a polynomial algorithm to verify the existence of a system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show how to use Interval Markov Chains to model abstractions of deterministic systems with confidential data, and use the above results to compute their channel capacity. These results are a foundation for ongoing work on computing channel capacity for abstractions of programs derived from code.

Abstract: General purpose theorem provers provide advanced facilities for proving properties about specifications, and may therefore be a valuable tool in formal program development. However, these provers generally lack many of the useful structuring mechanisms found in functional programming or specification languages. This paper presents a constructive approach to adding theory morphisms and parametrisation to theorem provers, while preserving the proof support and consistency of the prover. The approach is implemented in Isabelle and illustrated by examples of an algorithm design rule and of the modular development of computational effects for imperative language features based on monads.