Abstract
Formalization has a central role in computer science. Communication between man and computers as well as information processing within computer systems require that concepts and objects of the application domain are formally represented through some artificial language. In the last fifty years, the development of formal models has concerned practically all aspects of human life, from computing to management, from work to playing games and sex. Such development is one of the important contributions of computer science to human epistemological and intellectual development which expands the powerful role that mathematical formalization has played through the centuries. In building a formal model of reality, though, an important issue arises, the complexity of the formal system that is adopted; in fact, the stronger the expressive power of the system, the higher the complexity of using the model. An “optimal” balance between expressive power and complexity is the key that explains the success of some formal systems and languages that are widely used in computer science and applications. After discussing the contrasting needs of expressiveness and computational tractability in the construction of formal models, in the paper two case studies are considered: formal Chomsky grammars and relational database languages, and the balance between expressive power and complexity for such systems is analyzed in greater detail. Finally, the concept of succinctness of a formal system is taken into consideration, and it is shown that the role of succinctness in affecting the complexity of formal systems is crucial.
The first author gratefully acknowledges the support of the Italian MURST National Project “Efficienza di algoritmi e progetto di strutture informative.” The second author has been partially supported by MURST and CNR.
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Ausiello, G., Cabibbo, L. (1999). Expressiveness and Complexity of Formal Systems. In: Carsetti, A. (eds) Functional Models of Cognition. Theory and Decision Library, vol 27. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9620-6_7
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DOI: https://doi.org/10.1007/978-94-015-9620-6_7
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