Separation logic is successful for software verification of heap-manipulating programs. Numbers are necessary to be added to separation logic for verification of practical software where numbers are important. However, properties of the validity such as decidability and complexity for separation logic with numbers have not been fully studied yet. This paper presents the translation of Pi-0-1 formulas in Peano arithmetic to formulas in a small fragment of separation logic with numbers, which consists only of the intuitionistic points-to predicate, 0 and the successor function. Then this paper proves that a formula in Peano arithmetic is valid in the standard model if and only if its translation in this fragment is valid in the standard interpretation. As a corollary, this paper also gives a perspective proof for the undecidability of the validity in this fragment. Since Pi-0-1 formulas can describe consistency of logical systems and non-termination of computations, this result also shows that these properties discussed in Peano arithmetic can also be discussed in such a small fragment of separation logic with numbers.

Abstract Realizability is an important requirement for reactive system specifications. A reactive system interacts with an environment and responds to input events. Realizability ensures the reactive system behaves as specified, no matter how its environment provides input. Typically, reactive system specifications are given using linear temporal logic (LTL), and they can be tested to ascertain whether the specification is realizable. However, the LTL specification realizability problem is 2EXPTIME-complete, which hinders its application to large-scale systems. In this article, we present a modularization method to mitigate this computational challenge.

In this paper we present a conceptual model of fishery based on Resource-Event-Agent (REA) framework. We identify the concepts and relationships among them existing in fishery. The knowledge structure of fishery is formally presented so that the conceptual model be a formal ontology. For this, we introduce a formal semantic structure and a logical language. The meaning of the fishery-specific concepts and relationships is described as logical axioms. Through this formal approach, we discuss the adequateness and compatibility of REA framework to model fishery.

In this article we propose a novel formalism to model and analyse gene regulatory networks using a well-established formal verification technique. We model the possible behaviours of networks by logical formulae in linear temporal logic (LTL). By checking the satisfiability of LTL, it is possible to check whether some or all behaviours satisfy a given biological property, which is difficult in quantitative analyses such as the ordinary differential equation approach. Owing to the complexity of LTL satisfiability checking, analysis of large networks is generally intractable in this method. To mitigate this computational difficulty, we developed two methods. One is a modular checking method where we divide a network into subnetworks, check them individually, and then integrate them. The other is an approximate analysis method in which we specify behaviours in simpler formulae which compress or expand the possible behaviours of networks. In the approximate method, we focused on network motifs and presented approximate specifications for them. We confirmed by experiments that both methods improved the analysis of large networks.

We developed a method for analyzing the dynamics of gene regulatory networks in purely qualitative fashion. In our method, constraints for possible behaviors of a network and a biological property of interest are described as Linear Temporal Logic formulas, being automatically analyzed by satisfiability checking. In this way, we can investigate whether there exists some behavior which satisfies a specified property or whether all the behaviors satisfy a specified property, which are difficult in quantitative analysis.