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Reasoning about state machines in higher-order logic

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Book cover Hardware Specification, Verification and Synthesis: Mathematical Aspects

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 408))

Abstract

The promise of cost savings and guaranteed product reliability that have been claimed for formal verification of digital hardware have yet to be realised in practice. Largely, this is because it can be extraordinarily difficult and tedious verifying even a simple design. A large part of this difficulty is caused by the absence of much of real-world engineering theory in available theorem provers. The paper describes the formalisation of deterministic and non-deterministic state-machine theory in the HOL theorem prover. Proofs using the theory are not only shorter, but are much more tractable, and follow standard engineering reasoning much more closely than direct proofs without using the theory.

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References

  1. Martín Abadi and Leslie Lamport. The Existence of Refinement Mappings. SRC Report 29, Digital Equipment Corporation, 1988.

    Google Scholar 

  2. Robert S. Boyer and J. Strother Moore. A Computational Logic. Academic Press, 1979.

    Google Scholar 

  3. Alexandre Bronstein and Carolyn L. Talcott. String-Functional Semantics for Formal Verification of Synchronous Circuits. Report STAN-CS-88-1210, Stanford University Department of Computer Science, 1988.

    Google Scholar 

  4. M. C. Browne and E. M. Clarke. SML — a high level language for the design and verification of finite state machines. In D. Borrione, editor, IFIP International Working Conference: From HDL Descriptions to Guaranteed Circuit Designs, Elsevier Science Publishers B. V. (North-Holland), 1987.

    Google Scholar 

  5. Albert Camilleri, Mike Gordon, and Tom Melham. Hardware verification using higher-order logic. In D. Borrione, editor, IFIP International Working Conference: From HDL Descriptions to Guaranteed Circuit Designs, Elsevier Science Publishers B. V. (North-Holland), September 1987.

    Google Scholar 

  6. Avra. J. Cohn. A proof of correctness of the viper microprocessor: the first level. In G. Birwistle and P. A. Subrahmanyam, editors, VLSI Specification, Verification and Synthesis, Kluwer Academic Publishers, 1988.

    Google Scholar 

  7. Srinivas Devadas, Hi Keung Ma, and A. Richard Newton. On the Verification of Sequential Machines at Differing Levels of Abstraction. Memorandum UCB/ERL M86/93, University of California, Berkeley, 1986.

    Google Scholar 

  8. Michael J.C. Gordon. The denotational semantics of sequential machines. Information Processing Letters, 10(1), February 1980.

    Google Scholar 

  9. Mike Gordon. HOL: A Machine Oriented Formulation of Higher-Order Logic. Technical Report 68, University of Cambridge Computer Laboratory, 1985.

    Google Scholar 

  10. Mike Gordon. HOL: a proof generating system for higher-order logic. In G. Birwistle and P. A. Subrahmanyam, editors, VLSI Specification, Verification and Synthesis, Kluwer Academic Publishers, 1988.

    Google Scholar 

  11. Mike Gordon. Why higher-order logic is a good formalism for specifying and verifying hardware. In G. Milne and P. A. Subrahmanyam, editors, Formal Aspects of VLSI Design, North-Holland, 1986.

    Google Scholar 

  12. J. J. Joyce, G. Birtwistle, and M. Gordon. Verification and implementation of a microprocessor. In G. Birwistle and P. A. Subrahmanyam, editors, VLSI Specification, Verification and Synthesis, Kluwer Academic Publishers, 1988.

    Google Scholar 

  13. Paul Loewenstein. The formal verification of state-machines using higher-order logic. In IEEE International Conference on Computer Design, 1989.

    Google Scholar 

  14. G. L. Peterson. Myths about the mutual exclusion problem. Information Processing Letters, 12(3):115–116, 1981.

    Google Scholar 

  15. Mary Sheeran. μFP — An Algebraic VLSI Design Language. Technical Monograph PRG-39, Oxford University Computing Laboratory, 1983.

    Google Scholar 

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Miriam Leeser Geoffrey Brown

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© 1990 Springer-Verlag Berlin Heidelberg

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Loewenstein, P. (1990). Reasoning about state machines in higher-order logic. In: Leeser, M., Brown, G. (eds) Hardware Specification, Verification and Synthesis: Mathematical Aspects. Lecture Notes in Computer Science, vol 408. Springer, New York, NY. https://doi.org/10.1007/0-387-97226-9_24

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  • DOI: https://doi.org/10.1007/0-387-97226-9_24

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97226-8

  • Online ISBN: 978-0-387-34801-8

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