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Representational and Denotational Semantics of Digital Systems
July 1989 (vol. 38 no. 7)
pp. 986-999
The input/output transformation effected by digital systems can be considered as concrete realizations of abstract mathematical functions. The mappings between abstract functions and concrete realizations, if kept explicit throughout the formulation, constitute the necessary 'handles' (embodied by function definitions) for transformational reasoning about digital systems. Deductive reasoning ca

[1] M. A. Arbib,Theories of Abstract Automata. Englewood Cliffs, NJ: Prentice-Hall, 1968.
[2] A. Avizienis, "Signed-digit number representations for fast parallel arithmetic,"IRE Trans. Electron. Comput., vol. EC-10, pp. 389- 400, Sept. 1961.
[3] J. Backus, "Can programming be liberated from the von Neumann style? A functional style and its algebra of programs,"Commun. ACM, vol. 21, no. 8, pp. 613-641, Aug. 1978.
[4] R. T. Boute, "Towards a theory of system semantics-An introductory overview of the key concepts for communications engineers," Rep. RTB 8011, Bell Telephone Mfg. Cy, Antwerpen, Nov. 1980.
[5] R. T. Boute, "Functional description of digital systems,"Methodologies for Computer System Design, W. K. Giloi and B. D. Shriver, Eds. Amsterdam, North-Holland, 1985, pp. 291-306.
[6] R. T. Boute, "Current work on the semantics of digital systems," inFormal Aspects of VLSI Design, G. Milne and P. A. Subrahmanyam, Eds. Amsterdam, North-Holland, 1986, pp. 99-112.
[7] R. T. Boute, "System semantics and formal circuit description,"IEEE Trans. Circuits Syst., vol. CAS-33, Dec. 1986.
[8] R. T. Boute, "Representational and denotational semantics of digital systems," Rep. IR-61, Dep. Comput. Sci., Univ. of Nijmegen, July 1986.
[9] J. De Man, "The description of digital systems by means of a functional language,"Int. Rep., Bell Telephone Mfg. Cy, Antwerpen, 1986.
[10] Federal Information Processing Standards,Specifications for the Data Encryption Standard, FIPS Publ. 46, (Jan. 15, 1977).
[11] M. A. Breuer and A. D. Friedman,Diagnosis and Reliable Design of Digital Systems, London, England: Pitman, 1976.
[12] S. Ginsburg, "Abstract machines: A generalization of sequential machines," inProc. Symp. Math. Thy. Automata, Polytech. Inst. of Brooklyn, Apr. 1962, pp. 125-138.
[13] J. A. Goguen, J. W. Thatcher, E. Wagner, and J. B. Wright, "Initial algebra semantics and continuous algebras,"J. ACM, vol. 24, no. 1, pp. 68-95, 1977.
[14] M. J. C. Gordon, "The denotational semantics of sequential machines,"Inform. Processing Lett., vol. 10, pp. 1-3, Feb. 1980.
[15] J. Guttag, "Abstract data types and the development of data structures,"Commun. ACM, vol. 20, pp. 396-404, June 1977.
[16] C. A. R. Hoare, "Proof of correctness of data representations,"Acta Informatica, vol. 1, pp. 271-281, 1972.
[17] K. Hwang,Computer Arithmetic: Principles, Architecture, and Design. New York: Wiley, 1979.
[18] L. Meertens, "Algorithmics," inMathematics and Computer Science Proc. CWI Symp., J. W. de Bakkeret al., Eds., Nov. 1983, Amsterdam: North-Holland, 1986.
[19] A. J. R. G. Milner, "Processes: A mathematical model for computing agents," inLogic Colloquium '73, H. E. Rose and J. C. Shepherdson, Eds., Amsterdam, North-Holland, 1975, pp. 157-174.
[20] W. Neu and A. Kündig, "Project for a digital telephone network,"IEEE Trans. Comput. Technol., vol. COM-16, pp. 633-648, Oct. 1968.
[21] W. W. Peterson and E. J. Weldon,Error-Correcting Codes, 2nd. rev. ed. Cambridge, MA: MIT Press, 1972.
[22] B. Schoenmakers, student term project, Eindhoven Univ. of Technol., May 1986.
[23] E. P. Stabler, "System description languages,"IEEE Trans. Comput., vol. C-19, pp. 1160-1173, Dec. 1970.
[24] T. A. Standish, "Data structures--an axiomatic approach," inCurrent trends in Programming Methodology, Vol. IV: Data Structuring, R. T. Yeh, Ed. Englewood Cliffs, NJ: Prentice-Hall, 1978, pp. 30- 59.
[25] J. E. Stoy,Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory. Cambridge, MA: MIT Press, 1977.
[26] N. Takagi, H. Yasuura, and S. Yajima, "High-speed VLSI multiplication algorithm with a redundant binary addition tree,"IEEE Trans. Comput., vol. C-34, no. 9, pp. 789-796, Sept. 1985.
[27] D. A. Turner,SASL Language Manual, revised version, Univ. of Kent, 1979.
[28] D. A. Turner, "Miranda: A nonstrict functional language with polymorphic types," inConf. Functional Program. Lang. Comput. Architecture, Nancy, France, Sept. 1985, pp. 1-16.
[29] H. J. J. Te Riele, "Perfect numbers and aliquot sequences," inComputational Methods in Number Theory, H. W. Lenstra Jr. and R. Tijdeman, Eds., MC Tract 154 (part I), MC Tract 155 (part II), Centrum voor Wiskunde en Informatica, Amsterdam, 1982.
[30] S.D. Johnson,Synthesis of Digital Designs From Recursion Equations, MIT Press, Cambridge, Mass., 1984.
[31] M. Sheeran, "µFP: A language for VLSI design," inProc. 1984 ACM Symp. LISP and Functional Programming, Aug. 1984, pp. 104-112.

Index Terms:
representational semantics; denotational semantics; digital systems; input/output transformation; abstract mathematical functions; mappings; function definitions; functional recast; digital arithmetic; digital systems; number theory.
R.T. Boute, "Representational and Denotational Semantics of Digital Systems," IEEE Transactions on Computers, vol. 38, no. 7, pp. 986-999, July 1989, doi:10.1109/12.30850
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