A Dynamic Algebraic Specification for Social Networks

📝 Abstract

With the help of the Internet, social networks have grown rapidly. This has increased security requirements. We present a formalization of social networks as composite behavioral objects, defined using the Observational Transition System (OTS) approach. Our definition is then translated to the OTS/CafeOBJ algebraic specification methodology. This translation allows the formal verification of safety properties for social networks via the Proof Score method. Finally, using this methodology we formally verify some security properties.

💡 Analysis

With the help of the Internet, social networks have grown rapidly. This has increased security requirements. We present a formalization of social networks as composite behavioral objects, defined using the Observational Transition System (OTS) approach. Our definition is then translated to the OTS/CafeOBJ algebraic specification methodology. This translation allows the formal verification of safety properties for social networks via the Proof Score method. Finally, using this methodology we formally verify some security properties.

📄 Content

A Dynamic Algebraic Specification for Social Networks Katerina Ksystra1, Konstantinos Barlas1, Nikolaos Triantafyllou1 and Petros Stefaneas2,
1 School of Electrical and Computer Engineering, National Technical University of Athens, Heroon Polytechniou 9, 15780 Zografou, Athens, Greece {nitriant, kosbarl, katksy}@central.ntua.gr 2 School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Heroon Polytechniou 9, 15780 Zografou, Athens, Greece petros@math.ntua.gr Abstract. With the help of the Internet, social networks have grown rapidly. This has increased security requirements. We present a formalization of social networks as composite behavioral objects, defined using the Observational Transition System (OTS) approach. Our definition is then translated to the OTS/CafeOBJ algebraic specification methodology. This translation allows the formal verification of safety properties for social networks via the Proof Score method. Finally, using this methodology we formally verify some security properties.
Keywords: social networks, formal methods, algebraic specifications, CafeOBJ, OTS, proof scores, behavioral object composition. 1 Introduction A Social Network is a very broad term and can usually be defined in any of the following three ways: Social Network as a set of relationships: More formally, it contains a set of objects (nodes, representing individuals) and a mapping or description of relations (usually representing types of interdependency such as friendship or common interests) between the object or nodes. [16] Social Networking Service as an online representation: consists of a representation of a user (via a profile), his/her connections to other profiles, social links, and a variety of additional services.
Social Networking Sites as web-based services: they allow individuals to construct a public or semi-public profile within a bounded system, articulate a list of other users with whom they share a connection, and view and traverse their list of connections and those made by others within the system. The nature and nomenclature of these connections may vary from site to site [17]. While the concept of social networks originates back to the 19th century (a social network can represent various concepts, such as the relationship of a teacher and his/her students, a family, etc.), it’s only recently received a huge popularity boost with the help of the internet. Nowadays, the strain that the millions of users put on the structures of those (online) services is sometimes difficult to handle. Due to the 2

problems arising with this increase of use, several attempts have been made over the last years to describe and analyze the structure and properties of a social network as a formal concept. Our approach is based on formal methods, mathematically-based techniques that are used in the specification, development and verification of software and hardware systems. Papers related to the mathematical modeling of Social Networks include [14, 15]. [14] attempts to visualize and reduce the size of social networks with the help of formal concept analysis. It regards a social network as a static structure, examining snapshots (taken at a certain moment) and produce results based on that instance, but do not consider the network evolution in their approach. In [15] the authors suggest that formal methods can provide a logical foundation in order to express and enforce privacy and security policies on social networks, however the specification done is quite minimal and its extension relies on external tools such as Java. Our approach differs in the sense that we regard the social network as a dynamic composition of behavioral objects, specifically as profiles that are connected through friendship relationships and that the network evolves by adding or deleting profiles. The rest of the paper is organized as follows: Section 2 describes the mathematical background for observational transition systems (OTS), a quick introduction to the theory behavioral object composition and an abstract definition of a social network as an OTS. Section 3 provides an overview of the CafeOBJ specification language/system and the implementation of OTSs in this framework. Section 4 describes our modeling proposal while section 5 demonstrates how critical safety properties of our system can be verified. Finally, section 6 concludes our paper with some future goals.
2 A Social network as an OTS
An Observational Transition System, or OTS [12, 13], is a transition system that can be written in terms of equations. We assume that there exists a universal states space and that each data type we need to use in our OTS, including their equivalence relationship, has been declared in advance. An OTS is defined as the triplet where:

1. is a finite set of observers. Each is a function , where D is a data type that

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