Toshinori Takai

Right-Linear Finite Path Overlapping Term Rewriting Systems Effectively Preserve Recognizability

Right-linear finite path overlapping TRS are shown to effectively preserve recognizability. The class of right-linear finite path overlapping TRS properly includes the class of linear generalized semi-monadic TRS and the class of inverse left-linear growing TRS, which are known to effectively preserve recognizability. Approximations by inverse right-linear finite path overlapping TRS are also discussed.

Layered Transducing Term Rewriting System and Its Recognizability Preserving Property

A term rewriting system which effectively preserves recognizability (EPR-TRS) has good mathematical properties. In this paper, a new subclass of TRSs, layered transducing TRSs (LT-TRSs) is defined and its recognizability preserving property is discussed. The class of LT-TRSs contains some EPR-TRSs, e.g., {f(x) ? f(g(x))} which do not belong to any of the known decidable subclasses of EPR-TRSs. Bottom-up linear tree transducer, which is a well-known computation model in the tree language theory, is a special case of LT-TRS. We present a sufficient condition for an LT-TRS to be an EPR-TRS. Also some properties of LT-TRSs including reachability are shown to be decidable.

Decidability and Closure Properties of Equational Tree Languages

Equational tree automata provide a powerful tree language framework that facilitates to recognize congruence closures of tree languages. In the paper we show the emptiness problem for AC-tree automata and the intersection-emptiness problem for regular AC-tree automata, each of which was open in our previous work, are decidable, by a straightforward reduction to the reachability problem for ground AC-term rewriting. The newly obtained results generalize decidability of so-called reachable property problem of Mayr and Rusinowitch. We then discuss complexity issue of AC-tree automata. Moreover, in order to solve some other questions about regular A- and AC-tree automata, we recall the basic connection between word languages and tree languages.

Monodic tree kleene algebra

We propose a quasi-equational sound axiomatization of regular tree languages, called monodic tree Kleene algebra. The algebra is weaker than Kleene algebra introduced by Kozen. We find a subclass of regular tree languages, for which monodic tree Kleene algebra is complete. While regular tree expressions may have two or more kinds of place holders, the subclass can be equipped with only one kind of them. Along the lines of the original proof by Kozen, we prove the completeness theorem based on determinization and minimization of tree automata represented by matrices on monodic tree Kleene algebra.

A Verification Technique Using Term Rewriting Systems and Abstract Interpretation

Verifying the safety property of a transition system given by a term rewriting system is an undecidable problem. In this paper, we give an abstraction for the problem which is automatically generated from a given TRS by using abstract interpretation. Then we show that there are some cases in which the problem can be decided. Also we show a new decidable subclass of term rewriting systems which effectively preserves recognizability.

ACTAS: A System Design for Associative and Commutative Tree Automata Theory

ACTAS is an integrated system for manipulating associative and commutative tree automata (AC-tree automata for short), that has various functions such as for Boolean operations of AC-tree automata, computing rewrite descendants, and solv- ing emptiness and membership problems. In order to deal with high-complexity problems in reasonable time, over- and under-approximation algorithms are also equipped. Such functionality enables us automated verification of safety property in infinite state models, that is helpful in the domain of, e.g. network security, in particular, for security problems of cryptographic protocols allowing an equational property. In runtime of model construction, a tool support for analysis of state space expansion is provided. The intermediate status of the computation is dis- played in numerical data table, and also the line graphs are generated. Besides, a graphical user interface of the system provides us a user-friendly environment for handy use.

Linking Traceability with GSN

Regulations/standards for safety critical systems mandate the submission of safety cases. Even though safety cases are the basic framework for assuring the safety of systems, how they fit into other methods/techniques which ensure the quality of the system is not certain. Ensuring traceability is of particular importance, since traceability can help analyze relationships between artifacts (evidence in safety cases) in meaningful ways. However, it is not well understood how traceability and safety cases are related and how they can benefit each other. To remedy this situation, we present a meta-model which describes the relationship between the two and present a case study taken from IEC 62278/EN 50126 from railway systems to show how traceability and safety cases benefit each other in this paper.

A Supplemental Notation of GSN Aiming for Dealing with Changes of Assurance Cases

An assurance case is a document containing arguments about risk-related issues on a system and regarded as an effective means to achieve open systems dependability. This paper proposes a notation of an assurance case to deal with changes of a system which can pose challenges to an established assurance case. The proposed notation is based on GSN and the presented case study suggests that the notation can make change-management of assurance cases easier. We also show that a GSN with a confidence map can be expressed by the proposed notation.

Retrieving Information from a Document Repository for Constructing Assurance Cases

We address the problem of constructing an assurance case by presenting an approach to extract information from a large set of documents. In the proposed approach, document retrieval and formal concept analysis techniques are systematically combined for assisting users to explore relevant information from huge data set and to understand a number of concepts in such data set with the relation among them. We perform an experiment with a data set from an open-source software development project, in order to evaluate the effectiveness of our approach. The experimental results suggest that the proposed approach can be effective in terms of reducing the time and the cost for constructing assurance cases with acceptable confidence level, indicated by some assurance case quality metrics.