# A classification of symbolic transition systems

Henzinger TA, Majumdar R. 2000. A classification of symbolic transition systems. Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science. STACS: Theoretical Aspects of Computer Science, LNCS, vol. 1770, 13–34.

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Author

Henzinger, Thomas A

^{ISTA}^{}; Majumdar, RitankarSeries Title

LNCS

Abstract

We define five increasingly comprehensive classes of infinite-state systems, called STS1–5, whose state spaces have finitary structure. For four of these classes, we provide examples from hybrid systems.
STS1 These are the systems with finite bisimilarity quotients. They can be analyzed symbolically by (1) iterating the predecessor and boolean operations starting from a finite set of observable state sets, and (2) terminating when no new state sets are generated. This enables model checking of the μ-calculus.
STS2 These are the systems with finite similarity quotients. They can be analyzed symbolically by iterating the predecessor and positive boolean operations. This enables model checking of the existential and universal fragments of the μ-calculus.
STS3 These are the systems with finite trace-equivalence quotients. They can be analyzed symbolically by iterating the predecessor operation and a restricted form of positive boolean operations (intersection is restricted to intersection with observables). This enables model checking of linear temporal logic.
STS4 These are the systems with finite distance-equivalence quotients (two states are equivalent if for every distance d, the same observables can be reached in d transitions). The systems in this class can be analyzed symbolically by iterating the predecessor operation and terminating when no new state sets are generated. This enables model checking of the existential conjunction-free and universal disjunction-free fragments of the μ-calculus.
STS5 These are the systems with finite bounded-reachability quotients (two states are equivalent if for every distance d, the same observables can be reached in d or fewer transitions). The systems in this class can be analyzed symbolically by iterating the predecessor operation and terminating when no new states are encountered. This enables model checking of reachability properties.

Publishing Year

Date Published

2000-01-01

Proceedings Title

Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science

Acknowledgement

This research was supported in part by the DARPA (NASA) grant NAG2-1214, the DARPA (Wright-Patterson AFB) grant F33615-C-98-3614, the MARCO grant 98-DT-660, the ARO MURI grant DAAH-04-96-1-0341, and the NSF CAREER award CCR-9501708.

Volume

1770

Page

13 - 34

Conference

STACS: Theoretical Aspects of Computer Science

Conference Location

Lille, France

Conference Date

2000-02-17 – 2000-02-19

ISBN

IST-REx-ID

### Cite this

Henzinger TA, Majumdar R. A classification of symbolic transition systems. In:

*Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science*. Vol 1770. Springer; 2000:13-34. doi:10.1007/3-540-46541-3_2Henzinger, T. A., & Majumdar, R. (2000). A classification of symbolic transition systems. In

*Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science*(Vol. 1770, pp. 13–34). Lille, France: Springer. https://doi.org/10.1007/3-540-46541-3_2Henzinger, Thomas A, and Ritankar Majumdar. “A Classification of Symbolic Transition Systems.” In

*Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science*, 1770:13–34. Springer, 2000. https://doi.org/10.1007/3-540-46541-3_2.T. A. Henzinger and R. Majumdar, “A classification of symbolic transition systems,” in

*Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science*, Lille, France, 2000, vol. 1770, pp. 13–34.Henzinger, Thomas A., and Ritankar Majumdar. “A Classification of Symbolic Transition Systems.”

*Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science*, vol. 1770, Springer, 2000, pp. 13–34, doi:10.1007/3-540-46541-3_2.