Observational Transition Systems Research Articles

Formal Verification of Multitask Hybrid Systems by the OTS/CafeOBJ Method

Hybrid systems combine both continuous and discrete behaviors, which occur frequently in safety-critical applications in various domains including Internet-of-Things (IoT) and Cyber-Physical Systems (CPS) applications such as health care, transportation, and robotics. For safe and reliable information society with IoT and CPS technologies, it is important to establish a way to specify and verify hybrid systems formally. Formal descriptions of hybrid systems may help us to verify desired properties of a given system formally with computer supports. We propose a way to describe a formal specification of a given multitask hybrid system as an observational transition system (OTS) in CafeOBJ algebraic specification language. OTSs are models where systems behaviors are described through observations. CafeOBJ supports specification execution based on a rewrite theory. We verify that OTS/CafeOBJ specifications of hybrid systems satisfy desired property by the proof score method based on equational reasoning implemented in CafeOBJ interpreter. In this paper, we specify a signal control system with an arbitrary number of vehicles by our proposed method, and verify the system satisfies a safety property by the proof score method.

Model checking the iKP electronic payment protocols

Much progress of formal verification techniques has been made and therefore many formal verification case studies of systems, such as security protocols, have been conducted and reported. Two major formal verification techniques are model checking and interactive theorem proving. Almost all case studies, however, use either model checking or interactive theorem proving. Even though both techniques are used, two different specifications dedicated to model checking and interactive theorem proving, respectively, are used. It would be desirable to make it possible to use one specification for one system for both model checking and interactive theorem proving. Observational transition systems (OTSs) have been proposed so that they can be written as equational theory specifications and used for interactive theorem proving. OTSs can also be written as rewrite theory specifications, which can be used for model checking, but it would take time to model check OTSs written as rewrite theory specifications in the existing techniques.There are two main contributions described in this article: (1) to propose an effective way to write OTSs as rewrite theory specifications, and (2) to conduct a case study in which an electronic commerce protocol has been model checked. Contribution (1) can be regarded as an effective way to translate equational theory specifications of OTSs for interactive theorem proving into rewrite theory specifications of OTSs for model checking. Moreover, since rewrite theory specifications of OTSs can be used for interactive theorem proving as well, contribution (1) may lead to the desirable situation aforementioned.

An Algebraic Framework for the Verification of Context-Aware Adaptive Systems

Context-aware and self adaptive systems have become very popular during the last decade. As these technologies are increasingly used in the development of critical applications, their behavior should be extensively analyzed. While formal methods provide a wide range of techniques for reasoning about software systems, addressing formally the requirements of context-aware adaptive systems in a consistent way remains a challenge. To this end, in this paper we present an algebraic framework for their formal specification using Observational Transition Systems (OTSs) specified in the CafeOBJ algebraic specification language. This approach permits the verification of the design of such systems, and can be an effective approach to obtaining verified context-aware software. We apply the proposed framework to the modeling of a context-aware adaptive traffic monitoring system and use theorem proving techniques to prove safety properties for that system.

Compositionally Writing Proof Scores of Invariants in the OTS/CafeOBJ Method

Observational transition systems (OTSs) are state machines that can be described as behavioral specifications in CafeOBJ, an algebraic specification language and processor. The OTS/CafeOBJ method uses OTSs and CafeOBJ for systems spec- ification and verification. Simultaneous induction is intensively used to prove that an OTS enjoys invariants in the method. To prove that two state predicates p and q are invariants with respect to an OTS S, simultaneous induction generates the proof obli- gations: (1) p(υ0 )a ndp(υ) ∧ q(υ) ⇒ p(υ � ), and (2) q(υ0 )a ndp(υ) ∧ q(υ) ⇒ q(υ � ) for each initial state υ0, each state υ and each successor state υ � of υ .I nstead, we may also use the proof obligations: (1) q(υ) ⇒ p(υ), and (2) q(υ0 )a ndp(υ) ∧ q(υ) ⇒ q(υ � ). The proof technique generating proof obligations like this is called semi-simultaneous induction. The proof obligation is equivalent to (1) q(υ) ⇒ p(υ), and (2) q(υ0 )a nd q(υ) ⇒ q(υ � ). But, the former may need less cases, making proofs shorter, than the latter. More importantly, the former makes it possible to record the process in which way lemmas have been conjectured. This article demonstrates some benefits of (semi- )simultaneous induction, describes semi-simultaneous induction and justifies it.

Initial semantics in logics with constructors

The constructor-based logics constitute the logical foundation of the so-called OTS/CafeOBJ method, a modelling, specification and verification method of the observational transition systems. The important role played in algebraic specifications by the initial algebras semantics is well known. Free models along presentation morphisms provide semantics for the modules with initial denotation in structured specification languages. Following Goguen and Burstall, the notion of logical system over which we build specifications is formalized as an institution. The present work is an institution-independent study of the existence of free models along sufficient complete presentation morphisms in logics with constructors in the signatures.

An Algebraic Framework for Modeling of Mobile Systems

We present MobileOBJ, a formal framework for specifying and verifying mobile systems. Based on hidden algebra, the components of a mobile system are specified as behavioral objects or Observational Transition Systems, a kind of transition system, enriched with special action and observation operators related to the distinct characteristics of mobile computing systems. The whole system comes up as the concurrent composition of these components. The implementation of the abstract model is achieved using CafeOBJ, an executable, industrial strength algebraic specification language. The visualization of the specification can be done using CafeOBJ graphical notation. In addition, invariant and behavioral properties of mobile systems can be proved through theorem proving techniques, such as structural induction and coinduction that are fully supported by the CafeOBJ system. The application of the proposed framework is presented through the modeling of a mobile computing environment and the services that need to be supported by the former.

Modeling and verification of real-time systems based on equations

We describe timed observational transition systems (TOTSs). TOTSs are written in terms of equations. By regarding equations as left-to-right rewrite rules, rewriting, together with induction and/or case analysis, can be used to verify that timing properties hold for TOTSs. Concretely, CafeOBJ, an algebraic specification language, is used to specify TOTSs and verify that TOTSs have timing properties by writing proofs, or proof scores. Two case studies are used to demonstrate how to model real-time systems based on TOTSs, specify TOTSs in CafeOBJ and verify that TOTSs have timing properties with the CafeOBJ system.

Rewriting-Based Verification of Authentication Protocols

We propose a method of formally analysing security protocols based on rewriting. The method is roughly as follows. A security protocol is modeled as an observational transition system, which is described in CafeOBJ. Proof scores showing that the protocol has safety (security) properties are then written in CafeOBJ and the proof scores are executed (rewritten) by the CafeOBJ system.