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Algebraic Specification of Computer Viruses and Their Environments

Matt Webster
Selected Papers from the First Conference on Algebra and Coalgebra in Computer Science Young Researchers Workshop ({CALCO}-jnr 2005). University of Wales Swansea Computer Science Report Series {CSR} 18-2005}, pp.99-113

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This paper introduces an approach to formal specification of computer viruses and their environments through the development of algebraic specifications using Gurevich's Abstract State Machines (ASMs) and Goguen's OBJ. Distributed ASMs are used to develop a model of an abstract computer virus, which through a process of refinement is converted into models of different virus types. Further refinement has resulted in an executable specification, written in the Abstract State Machine Language, AsmL. The models strengthen the thesis that any algorithm can be modelled at a natural abstraction level using an Abstract State Machine. The ASM models combined with the AsmL executable specification provide a complementary theoretical and experimental framework for proofs and experiments on computer viruses and their environments, as well as a useful means of classification of different computer viruses types. Next we look at a different approach to computer virus analysis using OBJ, which is used to specify computer viruses written in an ad hoc programming language, SPL. The OBJ specification is shown to be useful for the detection of a virus type that is particularly difficult to detect - the metamorphic computer virus (MCV). Finally, the usefulness of the two specifications for reasoning about computer viruses is discussed and in this regard the two formalisms are compared.

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