Computations and interaction

We enhance the notion of a computation of the classical theory of computing with the notion of interaction. In this way, we enhance a Turing machine as a model of computation to a Reactive Turing Machine that is an abstract model of a computer as it is used nowadays, always interacting with the user and the world

Characteristic invariants in Hennessy-Milner logic

In this paper, we prove that Hennessy–Milner Logic (HML), despite its structural limitations, is sufficiently expressive to specify an initial property φ0 and a characteristic invariant χI for an arbitrary finite-state process P such that φ0∧AG(χI) is a characteristic formula for P. This means that a process Q, even if infinite state, is bisimulation equivalent to P iff Q⊨φ0∧AG(χI). It follows, in particular, that it is sufficient to check an HML formula for each state of a finite-state process to verify that it is bisimulation equivalent to P. In addition, more complex systems such as context-free processes can be checked for bisimulation equivalence with P using corresponding model checking algorithms. Our characteristic invariant is based on so called class-distinguishing formulas that identify bisimulation equivalence classes in P and which are expressed in HML. We extend Kanellakis and Smolka’s partition refinement algorithm for bisimulation checking in order to generate concise class-distinguishing formulas for finite-state processes

On path-based coalgebras and weak notions of bisimulation

It is well known that the theory of coalgebras provides an abstract definition of behavioural equivalence that coincides with strong bisimulation across a wide variety of state-based systems. Unfortunately, the theory in the presence of so-called silent actions is not yet fully developed. In this paper, we give a coalgebraic characterisation of branching (delay) bisimulation in the context of labelled transition systems (fully probabilistic systems). It is shown that recording executions (up to a notion of stuttering), rather than the set of successor states, from a state is sufficient to characterise the respected bisimulation relations in both cases

Rooted Divergence-Preserving Branching Bisimilarity is a Congruence

We prove that rooted divergence-preserving branching bisimilarity is a congruence for the process specification language consisting of nil, action prefix, choice, and the recursion construct

Branching time and orthogonal bisimulation equivalence

We propose a refinement of branching bisimulation equivalence that we call orthogonal bisimulation equivalence. Typically, internal activity (i.e., the performance of $tau$-steps) may be compressed, but not completely discarded. Hence, a process with $tau$-steps cannot be equivalent to one without $tau$-steps. Also, we present a modal characterization of orthogonal bisimulation equivalence. This equivalence is a congruence for ACP extended with abstraction and priority operations. We provide a complete axiomatization, and describe some expressiveness results. Finally, we present the verification of a PAR protocol that is specified with use of priorities

Rooted Divergence-Preserving Branching Bisimilarity is a Congruence

We prove that rooted divergence-preserving branching bisimilarity is a congruence for the process specification language consisting of nil, action prefix, choice, and the recursion construct