A Logic with Reverse Modalities for History-preserving Bisimulations

We introduce event identifier logic (EIL) which extends Hennessy-Milner logic by the addition of (1) reverse as well as forward modalities, and (2) identifiers to keep track of events. We show that this logic corresponds to hereditary history-preserving (HH) bisimulation equivalence within a particular true-concurrency model, namely stable configuration structures. We furthermore show how natural sublogics of EIL correspond to coarser equivalences. In particular we provide logical characterisations of weak history-preserving (WH) and history-preserving (H) bisimulation. Logics corresponding to HH and H bisimulation have been given previously, but not to WH bisimulation (when autoconcurrency is allowed), as far as we are aware. We also present characteristic formulas which characterise individual structures with respect to history-preserving equivalences.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407

Linear and Branching System Metrics

We extend the classical system relations of trace\ud inclusion, trace equivalence, simulation, and bisimulation to a quantitative setting in which propositions are interpreted not as boolean values, but as elements of arbitrary metric spaces.\ud \ud Trace inclusion and equivalence give rise to asymmetrical and symmetrical linear distances, while simulation and bisimulation give rise to asymmetrical and symmetrical branching distances. We study the relationships among these distances, and we provide a full logical characterization of the distances in terms of quantitative versions of LTL and μ-calculus. We show that, while trace inclusion (resp. equivalence) coincides with simulation (resp. bisimulation) for deterministic boolean transition systems, linear\ud and branching distances do not coincide for deterministic metric transition systems. Finally, we provide algorithms for computing the distances over finite systems, together with a matching lower complexity bound

A Unifying Approach to Decide Relations for Timed Automata and their Game Characterization

In this paper we present a unifying approach for deciding various bisimulations, simulation equivalences and preorders between two timed automata states. We propose a zone based method for deciding these relations in which we eliminate an explicit product construction of the region graphs or the zone graphs as in the classical methods. Our method is also generic and can be used to decide several timed relations. We also present a game characterization for these timed relations and show that the game hierarchy reflects the hierarchy of the timed relations. One can obtain an infinite game hierarchy and thus the game characterization further indicates the possibility of defining new timed relations which have not been studied yet. The game characterization also helps us to come up with a formula which encodes the separation between two states that are not timed bisimilar. Such distinguishing formulae can also be generated for many relations other than timed bisimilarity.Comment: In Proceedings EXPRESS/SOS 2013, arXiv:1307.690

From Agent Game Protocols to Implementable Roles

kostas.stathis-at-cs.rhul.ac.uk Abstract. We present a formal framework for decomposing agent interaction protocols to the roles their participants should play. The framework allows an Authority Agent that knows a protocol to compute the protocol’s roles so that it can allocate them to interested parties. We show how the Authority Agent can use the role descriptions to identify problems with the protocol and repair it on the fly, to ensure that participants will be able to implement their role requirements without compromising the protocol’s interactions. Our representation of agent interaction protocols is a game-based one and the decomposition of a game protocol into its constituent roles is based upon the branching bisimulation equivalence reduction of the game. The work extends our previous work on using games to admit agents in an artificial society by checking their competence according to the society rules. The applicability of the overall approach is illustrated by showing how to decompose the NetBill protocol into its roles. We also show how to automatically repair the interactions of a protocol that cannot be implemented in its original form.

Game Characterization of Probabilistic Bisimilarity, and Applications to Pushdown Automata

We study the bisimilarity problem for probabilistic pushdown automata (pPDA) and subclasses thereof. Our definition of pPDA allows both probabilistic and non-deterministic branching, generalising the classical notion of pushdown automata (without epsilon-transitions). We first show a general characterization of probabilistic bisimilarity in terms of two-player games, which naturally reduces checking bisimilarity of probabilistic labelled transition systems to checking bisimilarity of standard (non-deterministic) labelled transition systems. This reduction can be easily implemented in the framework of pPDA, allowing to use known results for standard (non-probabilistic) PDA and their subclasses. A direct use of the reduction incurs an exponential increase of complexity, which does not matter in deriving decidability of bisimilarity for pPDA due to the non-elementary complexity of the problem. In the cases of probabilistic one-counter automata (pOCA), of probabilistic visibly pushdown automata (pvPDA), and of probabilistic basic process algebras (i.e., single-state pPDA) we show that an implicit use of the reduction can avoid the complexity increase; we thus get PSPACE, EXPTIME, and 2-EXPTIME upper bounds, respectively, like for the respective non-probabilistic versions. The bisimilarity problems for OCA and vPDA are known to have matching lower bounds (thus being PSPACE-complete and EXPTIME-complete, respectively); we show that these lower bounds also hold for fully probabilistic versions that do not use non-determinism