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The decision problem for branching time logic1,2

Published online by Cambridge University Press:  12 March 2014

Yuri Gurevich
Affiliation:
Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan 48109
Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem 91904, Israel

Abstract

The theory of trees with additional unary predicates and quantification over nodes and branches embraces a rich branching time logic. This theory was reduced in the companion paper to the first-order theory of binary, bounded, well-founded trees with additional unary predicates. Here we prove the decidability of the latter theory.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1985

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Footnotes

1

The results were obtained in principle during the Jerusalem Logic Year 1980–81 when both authors were fellows in the Institute for Advanced Studies of Hebrew University.

2

Supported in part by the US-Israel Binational Science Foundation.

References

REFERENCES

[DMT]Doner, J. E., Mostowski, A. and Tarski, A., The elementary theory of well-ordering-a metamathematical study, Logic Colloquium '77, North-Holland, Amsterdam, 1978, pp. 154.Google Scholar
[Eh]Ehrenfeucht, A., An application of games to the completeness problem for formalized theories, Fundamenta Mathematicae, vol. 49(1961), pp. 129141:CrossRefGoogle Scholar
[Gu]Gurevich, Y., Monadic second-order theories, Model-theoretical logics (Barwise, J. and Feferman, S., editors), Springer-Verlag, Berlin (to appear).Google Scholar
[Gu2]Gurevich, Y., Toward logic tailored for computational complexity, Logic Colloquium '83, Lecture Notes in Mathematics, Springer-Verlag, Berlin (to appear).Google Scholar
[GS]Gurevich, Y. and Shelah, S., To the decision problem for branching time logic, Foundations of logic and linguistics: Problems and their solutions, Plenum Press (to appear).Google Scholar
[Sh]Shelah, S., The monadic theory of order, Annals of Mathematics, ser. 2, vol. 102 (1975), pp. 379419.CrossRefGoogle Scholar