Skip to main content
×
Home

Programming Combinations of Deduction and BDD-based Symbolic Calculation

  • Michael J. C. Gordon (a1)
Abstract
Abstract

A generalisation of Milner's ‘LCF approach’ is described. This allows algorithms based on binary decision diagrams (BDDs) to be programmed as derived proof rules in a calculus of representation judgements. The derivation of representation judgements becomes an LCF-style proof by defining an abstract type for judgements analogous to the LCF type of theorems. The primitive inference rules for representation judgements correspond to the operations provided by an efficient BDD package coded in C (BuDDy). Proof can combine traditional inference with steps inferring representation judgements. The resulting system provides a platform to support a tight and principled integration of theorem proving and model checking. The methods are illustrated by using them to solve all instances of a generalised Missionaries and Cannibals problem.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Programming Combinations of Deduction and BDD-based Symbolic Calculation
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Programming Combinations of Deduction and BDD-based Symbolic Calculation
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Programming Combinations of Deduction and BDD-based Symbolic Calculation
      Available formats
      ×
Copyright
References
Hide All
1Aagaard Mark D., Jones Robert B. and Seger Carl-Johan H., ‘Lifted-FL: a pragmatic implementation of combined model checking and theorem proving’, Theorem proving in higher order logics(TPHOLs99), Lecture Notes in Comput. Sci. 1690 (Springer, 1999) 323340.
2Amarel Saul, ‘On representation of problems of reasoning about action’, Machine intelligence 3 (ed. Michie Donald, Edinburgh University Press, 1971) 131171.
3Bryant Randall E., Symbolic boolean manipulation with ordered binary-decision diagrams, ACM Computing Surveys 24 (1992) 293318.
4Clarke Edmund M., Grumberg Orna and Peled Doron A., Model checking (The MIT Press, 1999).
5Coudert Olivier, Berthet Christian and Madre Jean Christophe, ‘Verification of synchronous sequential machines based on symbolic execution’, Automatic verification methods for finite state systems, Lecture Notes in Comput. Sci. 407 (ed. Sifakis J., Springer, 1989) 365373.
6Gordon Mike, ‘Reachability programming in HOL98 using BDDs’, Proc. 13th International Conference on Theorem Proving and Higher Order Logics (Springer, 2000) 179196.
7Gordon Mike, ‘HolBddLib’, http://www.cl.cam.ac.uk/~mjcg/HolBddLib/.
8Gordon M.J.C., Milner R. and Wadsworth C. P., Edinburgh LCF: a mechanised logic of computation, Lecture Notes in Comput. Sci. 78 (Springer, 1979).
9Harrison John, ‘Binary decision diagrams as a HOL derived rule’, The Computer Journal 38 (1995) 162170.
10Hazelhurst Scott, and Seger Carl-Johan H., ‘Symbolic trajectory evaluation’, Formal hardware verification (ed. Kropf Thomas, Springer, 1997) 378.
11Joyce J. and Seger C., ‘The HOL-Voss System: model-checking inside a general-purpose theorem-prover’, Higher order logic theorem proving and its applications, 6th International Workshop, HUG'93, Vancouver, B.C., August 1113 1993, Lecture Notes in Comput.Sci. 780 (ed. Joyce J. J. and Seger C.-J. H., Springer, 1994), 185’198.
12Lee Trevor W.S., Greenstreet Mark R. and Seger Carl-Johan, ‘Automatic verification of asynchronous circuits’, Tech. Rep. UBC TR 93–40, The University of British Columbia (November, 1993).
13McCarthy John, ‘Elaboration tolerance’, http://www-formal.stanford.edu/jmc/elaboration/node2.html.
14McMillan Kenneth L., Symbolic model checking (Kluwer Academic Publishers, 1993).
15McMillan K. L., ‘A compositional rule for hardware design refinement’, Computer- aided verification, CAV '97, Lecture Notes in Comput. Sci. (ed. Grumberg Orna, Springer, Haifa, Israel, 1997) 2435.
17Milner R., ‘A theory of type polymorphism in programming’, J.Comput.SystemSci 17 (1978) 348375.
18O'Leary John, Zhao Xudong, Gerth Robert and Seger Carl-Johan H., ‘For mally verifying IEEE compliance of floating-point hardware’, Intel Technology J., http://developer.intel.com/technology/itj/.
19Rajan S., Shankar N. and Srivas M. K., ‘An integration of model-checking with automated proof checking’, Computer-aided verification, CAV'95, Lecture Notes in Comput.Sci. 939 (ed. Wolper Pierre, Springer, Liege, Belgium, 1995) 8497.
20Seger Carl-Johan H., ‘VOSS - a formal hardware verification system: User's guide’, Tech. Rep UBC TR 93–45, The University of British Columbia, (December, 1993).
21International Sri, ‘PVS’, http://www.csl.sri.com/pvs.html.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

LMS Journal of Computation and Mathematics
  • ISSN: -
  • EISSN: 1461-1570
  • URL: /core/journals/lms-journal-of-computation-and-mathematics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 19 *
Loading metrics...

Abstract views

Total abstract views: 90 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 24th November 2017. This data will be updated every 24 hours.