Abstract: Basic properties of rewriting systems can be stated in the framework of abstract reduction systems (ARS). Properties like confluence (or Church-Rosser, CR) and weak confluence (or weak Church-Rosser, WCR) and their relationships can be studied in this setting: as a matter of fact, well-known counterexamples to the implication WCR CR have been formulated as ARS. In this paper, starting from the observation that such counterexamples are structurally similar, we set out a graph-theoretic characterization of WCR ARS that is not CR in terms of a suitable class of reduction graphs, such that in every WCR not CR ARS, we can embed at least one element of this class. Moreover, we give a tighter characterization for a restricted class of ARS enjoying a suitable regularity condition. Finally, as a consequence of our approach, we prove some interesting results about ARS using the mathematical tools developed. In particular, we prove an extension of the Newman’s lemma and we find out conditions that, once assumed together with WCR property, ensure the unique normal form property. The Appendix treats two interesting examples, both generated by graph-rewriting rules, with specific combinatorial properties.

Abstract: This paper presents a novel method for comparing computational properties of λ-terms that are typeable with intersection types, with respect to terms that are typeable with Curry types. We introduce a translation from intersection typing derivations to Curry typeable terms that is preserved by β-reduction: this allows the simulation of a computation starting from a term typeable in the intersection discipline by means of a computation starting from a simply typeable term. Our approach proves strong normalisation for the intersection system naturally by means of purely syntactical techniques. The paper extends the results presented in Bucciarelli et al. (1999) to the whole intersection type system of Barendregt, Coppo and Dezani, thus providing a complete proof of the conjecture, proposed in Leivant (1990), that all functions uniformly definable using intersection types are already definable using Curry types.

Abstract: SBML is the most widespread language for the definition of biochemical models. Although dozens of SBML simulators are available, there is a general lack of support to the integration of SBML models within open-standard general-purpose simulation ecosystems. This hinders co-simulation and integration of SBML models within larger model networks, in order to, e.g., enable in-silico clinical trials of drugs, pharmacological protocols, or engineering artefacts such as biomedical devices against Virtual Physiological Human models.Modelica is one of the most popular existing open-standard general-purpose simulation languages, supported by many simulators. Modelica models are especially suited for the definition of complex networks of heterogeneous models from virtually all application domains. Models written in Modelica (and in 100+ other languages) can be readily exported into black-box Functional Mock-Up Units (FMUs), and seamlessly co-simulated and integrated into larger model networks within open-standard language-independent simulation ecosystems.In order to enable SBML model integration within heterogeneous model networks, we present SBML2Modelica, a software system translating SBML models into well-structured, user-intelligible, easily modifiable Modelica models. SBML2Modelica is SBML Level 3 Version 2 -compliant and succeeds on 96.47% of the SBML Test Suite Core (with a few rare, intricate, and easily avoidable combinations of constructs unsupported and cleanly signalled to the user). Our experimental campaign on 613 models from the BioModels database (with up to 5438 variables) shows that the major open-source (general-purpose) Modelica and FMU simulators achieve performance comparable to state-of-the-art specialised SBML simulators.SBML2Modelica is written in Java and is freely available for non-commercial use at https://bitbucket.org/mclab/sbml2modelica

Abstract: In this paper we present an explicit disk-based verification algorithm for Probabilistic Systems defining discrete time/finite state Markov Chains. Given a Markov Chain and an integer k (horizon), our algorithm checks whether the probability of reaching an error state in at most k steps is below a given threshold. We present an implementation of our algorithm within a suitable extension of the Mur$\varphi$ verifier. We call the resulting probabilistic model checker FHP-Mur$\varphi$ (Finite Horizon Probabilistic Mur$\varphi$). We present experimental results comparing FHP-Mur$\varphi$ with (a finite horizon subset of) PRISM, a state-of-the-art symbolic model checker for Markov Chains. Our experimental results show that FHP-Mur$\varphi$ can handle systems that are out of reach for PRISM, namely those involving arithmetic operations on the state variables (e.g. hybrid systems).

Abstract: A Cyber-Physical System (CPS) comprises physical as well as software subsystems. Simulation-based approaches are typically used to support design and Verification and Validation (V&V) of CPSs in several domains such as: aerospace, defence, automotive, smart grid and healthcare. Accordingly, many simulation-based tools are available to support CPS design. This, on one side, enables designers to choose the toolchain that best suits their needs, on the other side poses huge interoperability challenges when one needs to simulate CPSs whose subsystems have been designed and modelled using different toolchains. To overcome such an interoperability problem, in 2010 the Functional Mock-up Interface (FMI) has been proposed as an open standard to support both Model Exchange (ME) and Co-Simulation (CS) of simulation models created with different toolchains. FMI has been adopted by several modelling and simulation environments. Models adhering to such a standard are called Functional Mock-up Units (FMUs). Indeed FMUs play an essential role in defining complex CPSs through, e.g., the System Structure and Parametrization (SSP) standard. Simulation-based V&V of CPSs typically requires exploring different simulation scenarios (i.e., exogenous input sequences to the CPS under design). Many such scenarios have a shared prefix. Accordingly, to avoid simulating many times such shared prefixes, the simulator state at the end of a shared prefix is saved and then restored and used as a start state for the simulation of the next scenario. In this context, an important FMI feature is the capability to save and restore the internal FMU state on demand. This is crucial to increase efficiency of simulation-based V&V. Unfortunately, the implementation of this feature is not mandatory and it is available only within some commercial software. As a result, the interoperability enabled by the FMI standard cannot be fully exploited for V&V when using open-source simulation environments. This motivates developing such a feature for open-source CPS simulation environments. Accordingly, in this paper, we focus on JModelica, an open-source modelling and simulation environment for CPSs based on an open standard modelling language, namely Modelica. We describe how we have endowed JModelica with our open-source implementation of the FMI 2.0 functions needed to save and restore internal states of FMUs for ME. Furthermore, we present experimental results evaluating, through 934 benchmark models, correctness and efficiency of our extended JModelica. Our experimental results show that simulation-based V&V is, on average, 22 times faster with our get/set functionality than without it.