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Engineering design is a computable function

Published online by Cambridge University Press:  27 February 2009

Patrick A. Fitzhorn
Patrick A. Fitzhorn
Affiliation:
Department of Mechanical Engineering, Colorado State University, Fort Collins, CO 80523.
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Abstract

Computational abstraction of engineering design leads to an elegant theory defining (1) the process of design as an abstract model of computability, the Turing machine; (2) the artifacts of design as enumerated strings from a (possibly multidimensional) grammar; and (3) design specifications or constraints as formal state changes that govern string enumeration. Using this theory, it is shown that engineering design is a computable function. A computational methodology based on the theory is then developed that can be described as a form follows function design paradigm.

Keywords

engineering designdesign artifactsTuring machinecomputable function

Information

Type
Research Article
Information
AI EDAM , Volume 8 , Issue 1 , Winter 1994 , pp. 35 - 44
Copyright
Copyright © Cambridge University Press 1994

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References

REFERENCES

Abe, N., Mizumoto, M., Toyoda, J., & Tanaka, K. (1973). Web grammars and several graphs. J. Comput. Syst. Sci. 7, 37–65.Google Scholar
Brainerd, W. (1969). Tree-generating regular systems. Inform. Contr. 74, 217–231.Google Scholar
Christakis, A., Keever, D., & Warfield, J. (1987). Development of generalized design theory and methodology. In The Study of the Design Process: A Workshop (Waldron, M., Ed.), pp. 3–72. The Ohio State University.Google Scholar
Feder, J. (1971). Plex languages. Inform. Sci. 3, 225–241.CrossRefGoogle Scholar
Fitzhorn, P. (1987). A linguistic formalism for engineering solid modeling. In Graph-Grammars and their Applications, (Ehrig, H., Nagl, M., & Rozenberg, C., Eds.), pp. 202–215. Springer-Verlag, New York.CrossRefGoogle Scholar
Fitzhorn, P. (1990). Language of topologically valid bounding manifolds. Computer-Aided Design 22 (7), 407–416.CrossRefGoogle Scholar
Fitzhorn, P. (1991). Formal graph languages of shape. Art. Intell, for Engin. Design, Analysis Manuf. 4 (3), 151–163.CrossRefGoogle Scholar
Gips, J. (1975). Shape Grammars and their Uses. Birkhauser-Verlag, Basel and Stuttgart.Google Scholar
Harrison, M. (1974). Some linguistic issues in design. In Basic Questions of Design Theory (Spillers, W., Ed.), pp. 405–415. North-Holland, Amsterdam.Google Scholar
Hatvany, J. (1987). An attempt at a holistic view of design. In Design Theory for CAD (Yoshikawa, H., & Warman, E., Eds.), pp. 131–135. North-Holland, Amsterdam.Google Scholar
Hopcroft, J., & Ullman, J. (1979). Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading, Massachusetts.Google Scholar
Janssens, D., & Rozenberg, G. (1986). Actor grammars: A graph grammar model for actor computation. In Third International Workshop on Graph Grammars, Warrenton, Virginia.Google Scholar
Kim, S. (1981). Mathematical foundations of manufacturing science: Theory and implications. Ph.D. Thesis. Massachusetts Institute of Technology, Cambridge, Massachusetts.Google Scholar
Lindenmayer, A. (1975). Developmental algorithms for multicellular organisms: A survey of 1-systems. J. Theoret. Bio. 54, 3–22.CrossRefGoogle Scholar
Lindenmayer, A., & Rozenberg, G. (1979). Parallel generation of maps: Developmental systems for cell layers. In Graph Grammars and their Applications to CS and Biology (Ehrig, H. et al. , Eds.), pp. 301–316. Springer-Verlag.Google Scholar
Longenecker, S., & Fitzhorn, P. (1989). Form + function + algebra = feature grammars. In Design Theory ’88 (Newsome, S. et al. , Eds.), pp. 189–197. Springer-Verlag.Google Scholar
Mantyla, M. (1984). A note on the modeling space of Euler operators. Comp. Vision, Graphics, Image Processing 26, 45–60.CrossRefGoogle Scholar
Nadler, G. (1981). The Planning and Design Approach. John Wiley, New York.Google Scholar
Nagl, M. (1979). A tutorial and bibliographical survey on graph grammars. In Graph Grammars and their Applications to CS and Biology (Ehrig, H. et al. , Eds.). Springer-Verlag.Google Scholar
Nyrup, K., & Mayoh, B. (1979). Map grammars: Cycles and the algebraic approach. In Graph Grammars and their Applications to CS and Biology (Ehrig, H. et al. , Eds.), pp. 331–340. Springer-Verlag.Google Scholar
Papalambros, P., & Wilde, D. (1988). Principles of Optimal Design. Cambridge University Press, New York.Google Scholar
Requicha, A.A.G. (1980). Representations of rigid solids: Theory, methods and systems. ACM Comput. Surv. 12, 437–464.Google Scholar
Siromoney, R., & Subramanian, K. (1983). Space-filling curves and infinite graphs. In Graph Grammars and their Application to Computer Science (Ehrig, H. et al. , Eds.), pp. 380–391. Springer-Verlag.CrossRefGoogle Scholar
Smith, A.R. (1984). Plants, fractals and formal languages. Comput. Graph. 18, 1–10.Google Scholar
Stiny, G. (1975). Pictorial and Formal Aspects of Shape and Shape Grammars. Birkhauser-Verlag, Basel and Stuttgart.Google Scholar
Stiny, G. (1980). An introduction to shape and shape grammars. Envir. Planning B 7, 343–351.CrossRefGoogle Scholar
Stiny, G. (1985). Computing with form and meaning in architecture. J. Archit. Ed. (Fall), 7–19.Google Scholar
Stiny, G., & Gips, J. (1978). Algorithmic Aesthetics. University of California Press, Berkeley, California.Google Scholar
Stiny, G., & March, L. (1981). Design machines. Envir. Planning B 8, 245–255.Google Scholar
Tomiyama, T., & Yoshikawa, H. (1987). Extended general design theory. In Design Theory for CAD (Yoshikawa, H., & Warman, E., Eds.), pp. 95–130. North-Holland, Amsterdam.Google Scholar
Whitley, D., Mathias, K., & Fitzhorn, P. (1991). Delta coding: An iterative strategy for genetic algorithms. In Proc. Fourth Ann. Conf. Genetic Algorithms (Belew, R., & Booker, L., Eds.). Morgan Kaufmann.Google Scholar