Non-null Infinitesimal Micro-steps: a Metric Temporal Logic Approach

Many systems include components interacting with each other that evolve with possibly very different speeds. To deal with this situation many formal models adopt the abstraction of "zero-time transitions", which do not consume time. These however have several drawbacks in terms of naturalness and logic consistency, as a system is modeled to be in different states at the same time. We propose a novel approach that exploits concepts from non-standard analysis to introduce a notion of micro- and macro-steps in an extension of the TRIO metric temporal logic, called X-TRIO. We use X-TRIO to provide a formal semantics and an automated verification technique to Stateflow-like notations used in the design of flexible manufacturing systems.Comment: 20 pages, 2 figures, submitted to the conference "FORMATS: Formal Modelling and Analysis of Timed Systems" 201

A temporal logic for micro- and macro-step-based real-time systems: Foundations and applications

Many systems include components interacting with each other that evolve at possibly very different speeds. To deal with this situation many formal models adopt the abstraction of “zero-time transitions”, which do not consume time. These, however, have several drawbacks in terms of naturalness and logic consistency, as a system is modeled to be in different states at the same time. We propose a novel approach that exploits concepts from non-standard analysis and pairs them with the traditional “next” operator of temporal logic to introduce a notion of micro- and macro-steps; our approach is enacted in an extension of the TRIO metric temporal logic, called X-TRIO. We study the expressiveness and decidability properties of the new logic. Decidability is achieved through translation of a meaningful subset of X-TRIO into Linear Temporal Logic, a traditional way to support automated verification. We illustrate the usefulness and the generality of our approach by applying it to provide a formal semantics of timed Petri nets, which allows for their automated verification. We also give an overview of a formal semantics of Stateflow/Simulink diagrams, defined in terms of X-TRIO, which has been applied to the automated verification of a robotic cell

Design-time formal verification for smart environments: an exploratory perspective

Smart environments (SmE) are richly integrated with multiple heterogeneous devices; they perform the operations in intelligent manner by considering the context and actions/behaviors of the users. Their major objective is to enable the environment to provide ease and comfort to the users. The reliance on these systems demands consistent behavior. The versatility of devices, user behavior and intricacy of communication complicate the modeling and verification of SmE's reliable behavior. Of the many available modeling and verification techniques, formal methods appear to be the most promising. Due to a large variety of implementation scenarios and support for conditional behavior/processing, the concept of SmE is applicable to diverse areas which calls for focused research. As a result, a number of modeling and verification techniques have been made available for designers. This paper explores and puts into perspective the modeling and verification techniques based on an extended literature survey. These techniques mainly focus on some specific aspects, with a few overlapping scenarios (such as user interaction, devices interaction and control, context awareness, etc.), which were of the interest to the researchers based on their specialized competencies. The techniques are categorized on the basis of various factors and formalisms considered for the modeling and verification and later analyzed. The results show that no surveyed technique maintains a holistic perspective; each technique is used for the modeling and verification of specific SmE aspects. The results further help the designers select appropriate modeling and verification techniques under given requirements and stress for more R&D effort into SmE modeling and verification researc

Modelling Statecharts and Activitycharts as Signal equations

International audienceThe languages for modeling reactive systems are of different styles, like the imperative, state-based ones and the declarative, data-flow ones. They are adapted to different application domains. This paper, through the example of the languages Statecharts and Signal, shows a way to give a model of an imperative specification (Statecharts) in a declarative, equational one (Signal). This model constitutes a formal model of the Statemate semantics of Statecharts, upon which formal analysis techniques can be applied. Being a transformation from an imperative to a declarative structure, it involves the definition of generic models for the explicit management of state (in the case of control as well as of data). In order to obtain a structural construction of the model, a hierarchical and modular organization is proposed, including proper management and propagation of control along the hierarchy. The results presented here cover the essential features of Statecharts as well as of another language of Statemate: Activitycharts. As a translation, it makes multiformalism specification possible, and provides support for the integrated operation of the languages. The motivation lies also in the perspective of gaining access to the various formal analysis and implementation tools of the synchronous technology, using the DC exchange format, as in the Sacres programming environment

A Complete Axiom System for Propositional Interval Temporal Logic with Infinite Time

Interval Temporal Logic (ITL) is an established temporal formalism for reasoning about time periods. For over 25 years, it has been applied in a number of ways and several ITL variants, axiom systems and tools have been investigated. We solve the longstanding open problem of finding a complete axiom system for basic quantifier-free propositional ITL (PITL) with infinite time for analysing nonterminating computational systems. Our completeness proof uses a reduction to completeness for PITL with finite time and conventional propositional linear-time temporal logic. Unlike completeness proofs of equally expressive logics with nonelementary computational complexity, our semantic approach does not use tableaux, subformula closures or explicit deductions involving encodings of omega automata and nontrivial techniques for complementing them. We believe that our result also provides evidence of the naturalness of interval-based reasoning

Behavior description and safety in real time models

This paper includes a survey on sorne modern methods that are used for describing and analyzing behavior of complex systems. It is believed that most safety problems arise in the interface between the controlling parts and other controlled subsystems. Therefore, a prerequisite for a good interface is an accurate definition of the system. Two objectives are evaluated: the description power and the analysis power for safety and timing properties. This is done by describing and analyzing a simple system that is composed of two doors, which are restricted by time and "safety" requirements. It is found that although good description methods do exist, their usefulness for analyzing safety timed properties is very limited