# On a Semantic Definition of Data Independence

## Abstract

A variety of results which enable model checking of important classes of infinite-state systems are based on exploiting the property of data independence. The literature contains a number of definitions of variants of data independence, which are given by syntactic restrictions in particular formalisms. More recently, data independence was defined for labelled transition systems using logical relations, enabling results about data independent systems to be proved without reference to a particular syntax. In this paper, we show that the semantic definition is sufficiently strong for this purpose. More precisely, it was known that any syntactically data independent symbolic LTS denotes a semantically data independent family of LTSs, but here we show that the converse also holds.

### Keywords

Data independence definability logical relations nondeterminism## Preview

Unable to display preview. Download preview PDF.

### References

- 1.M. Alimohamed. A characterization of lambda definability in categorical models of implicit polymorphism.
*Theoretical Computer Science*, 146:5–23, 1995.MATHCrossRefMathSciNetGoogle Scholar - 2.J. Bohn, W. Damm, O. Grumberg, H. Hungar, and K. Laster. First-order-CTL model checking. In
*Foundations of Software Technology and Theoretical Computer Science (FST&TCS’98)*, volume 1530 of*Lecture Notes in Computer Science*, pages 283–294. Springer-Verlag, 1998.Google Scholar - 3.M. Calder and C. Shankland. A symbolic semantics and bisimulation for full LOTOS. In
*International Conference on Formal Description Techniques for Networked and Distributed Systems (FORTE’01)*, pages 184–200. Kluwer Academic Publishers, 2001.Google Scholar - 4.K. M. Chandy and J. Misra.
*Parallel Program Design: A Foundation*. Addison-Wesley, 1988.Google Scholar - 5.E. M. Clarke, O. Grumberg, and D. A. Peled.
*Model Checking*. MIT Press, 1999.Google Scholar - 6.D. Dill, R. Hojati, and R.K. Brayton. Verifying linear temporal properties of data intensive controllers using finite instantiations. In
*Hardware Description Languages and their Applications (CHDL’ 97)*. Chapman and Hall, 1997.Google Scholar - 7.M. Fiore and A. Simpson. Lambda definability with sums via Grothendieck logical relations. In
*Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications (TLCA’99)*, volume 1581 of*Lecture Notes in Computer Science*, pages 147–161. Springer-Verlag, 1999.CrossRefGoogle Scholar - 8.J. Goubault-Larrecq, S. Lasota, and D. Nowak. Logical relations for monadic types. In
*Proceedings of the 11th Annual Conference of the European Association for Computer Science Logic (CSL’02)*, volume 2471 of*Lecture Notes in Computer Science*, pages 553-568. Springer-Verlag, 2002.Google Scholar - 9.M. Hennessy and H. Lin. Symbolic bisimulations.
*Theoretical Computer Science*, 138(2):353–389, 1995.MATHCrossRefMathSciNetGoogle Scholar - 10.C. N. Ip and D. L. Dill. Better verification through symmetry.
*Formal Methods in System Design: An International Journal*, 9(1/2):41–75, 1996.Google Scholar - 11.A. Jeffrey. A fully abstract semantics for a higher-order functional language with nondeterministic computation.
*Theoretical Computer Science*, 228:105–150, 1999.MATHCrossRefMathSciNetGoogle Scholar - 12.B. Jonsson and J. Parrow. Deciding bisimulation equivalences for a class of non-finite-state programs.
*Information and Computation*, 107(2):272–302, 1993.MATHCrossRefMathSciNetGoogle Scholar - 13.A. Jung and J. Tiuryn. A new characterization of lambda definability. In
*Proceedings of the 1st International Conference on Typed Lambda Calculi and Applications (TLCA’93)*, volume 664 of*Lecture Notes in Computer Science*, pages 245–257. Springer-Verlag, 1993.CrossRefGoogle Scholar - 14.R. Lazić.
*A Semantic Study of Data Independence with Applications to Model Checking*. DPhil thesis, Oxford University Computing Laboratory, 1999.Google Scholar - 15.R. Lazić and D. Nowak. A unifying approach to data-independence. In
*Proceedings of the 11th International Conference on Concurrency Theory (CONCUR 2000)*, volume 1877 of*Lecture Notes in Computer Science*, pages 581–595. Springer-Verlag, 2000.CrossRefGoogle Scholar - 16.R. Lazić and D. Nowak. On a semantic definition of data independence. Research report 392, Department of Computer Science, University of Warwick, 2003. http://www.dcs.warwick.ac.uk.
- 17.T. Nipkow. Non-deterministic data types: models and implementations.
*Acta Informatica*, 22(6):629–661, 1986.MATHCrossRefMathSciNetGoogle Scholar - 18.G. D. Plotkin. Lambda-definability in the full type hierarchy. In
*To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism*, pages 363–373. Academic Press, 1980.Google Scholar - 19.S. Qadeer. Verifying sequential consistency on shared-memory multiprocessors by model checking. Research Report 176, Compaq, 2001.Google Scholar
- 20.R. Hojati and R. K. Brayton. Automatic datapath abstraction in hardware systems. In
*Proceedings of the 7th International Conference On Computer Aided Verification*, volume 939 of*Lecture Notes in Computer Science*, pages 98–113. Springer Verlag, 1995.Google Scholar - 21.J. C. Reynolds. Types, abstraction and parametric polymorphism. In
*Proceedings of the 9th IFIP World Computer Congress (IFIP’83)*, pages 513–523. North-Holland, 1983.Google Scholar - 22.A. W. Roscoe and P. J. Broadfoot. Proving security protocols with model checkers by data independence techniques.
*Journal of Computer Security, Special Issue on the 11th IEEE Computer Security Foundations Workshop (CSFW11)*, pages 147–190, 1999.Google Scholar - 23.P. Wolper. Expressing interesting properties of programs in propositional temporal logic. In
*Conference Record of the 13th Annual ACM Symposium on Principles of Programming Languages*, pages 184–193. ACM, 1986.Google Scholar